the normalized correlation accounting for binaural detection across center frequency bernstein and trahiotis l r bernstein and c trahiotis j acoust soc am 100 1754 1763 1996 recently reported the results of experiments designed to determine the form of interaural correlation that accounts for listeners sensitivities to interaural disparities within high frequency stimuli overall those results demonstrated that listeners abilities to discriminate changes in the interaural correlation of the envelope from a base correlation of 1 0 were well accounted for by the use of the normalized correlation the purpose of this study was to determine how well the normalized correlation computed subsequent to half wave rectification and low pass filtering could account for binaural detection data at low intermediate and high frequencies respectively in a four interval two alternative task listeners detected which interval contained a tone between 500 hz and 2 khz added antiphasically to diotic 100 hz wide noise nos nonsignal intervals contained the tone added homophasically noso performance was measured for signal to noise ratios between 30 and 30 db results indicated that a low pass filter function based on physiological measures of synchrony in cochlear nerve fibers in conjunction with the assumption of half wave square law rectification accounted for typically 80 of the variance in the behavioral data

bifurcation analysis in van der pol s oscillator with delayed feedback in this paper a classical van der pol s equation with generally delayed feedback is considered it is shown that there are bogdanov takens bifurcation triple zero and hopf zero singularities by analyzing the distribution of the roots of the associated characteristic equation in the situation that the zero is as a simple eigenvalue the normal forms of the reduced equations are obtained by the center manifold theory and normal form method for functional differential equation and hence the stability of the fixed point is determined and transcritical and pitchfork bifurcations are found

explicit solutions of the discrete time lyapunov matrix equation and kalman yakubovich equations a general solution for the nonsquare nonsymmetric lyapunov matrix equation in a canonical form is presented the solution is shown to be a toeplitz matrix which may be calculated using the backwards levinson algorithm this solution is then applied to the kalman yakubovich equations to derive a method for generating strictly positive real functions via the positive real lemma this latter result has an application in system identification

multiple bifurcations in a delayed predator prey system with nonmonotonic functional response abstract a delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by faria and magalhaes the bifurcation analysis of the model indicates that there is a bogdanov takens singularity for any time delay value a versal unfolding of the model at the bogdanov takens singularity is obtained on the other hand it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit hopf bifurcation as the time delay passes through some critical values

lateralization of bands of noise as a function of combinations of interaural intensitive differences interaural temporal differences and bandwidth listeners indicated the intracranial position of bands of noise from 50 to 400 hz in width for several combinations of interaural intensitive differences iid and interaural temporal differences itd and or interaural phase differences ipd all itd and ipd combinations produced an interaural delay of 1500 s at the center frequency of the noise the interaural phase spectra were constructed to produce several patterns of putative cross correlation functions potency of iids depended greatly on particular combinations of bandwidth itd and ipd for some combinations changing the iid by only 3 db resulted in large shifts in laterality sometimes moving the image from near one ear to near the other the complex interactions observed make the results incompatible with the traditional notion that iids simply act as weights or scalars rather iids act in two distinct manners 1 as independent scalar quantities and 2 by interacting with specific combinations of bandwidth and itd ipd which is believed to reflect an action within the cross correlation surface

lateralization of complex binaural stimuli a weighted image model this article describes a new model that predicts the subjective lateral position of bandpass stimuli it is assumed as in other models that stimuli are bandpass filtered and rectified and that the rectified outputs of filters with matching center frequencies undergo interaural cross correlation the model specifies and utilizes the shape and location of assumed patterns of neural activity that describe the cross correlation function individual modes of this function receive greater weighting if they are straighter describing consistent interaural delay over frequency and or more central describing interaural delays of smaller magnitude this weighting of straightness and centrality is used by the model to predict the perceived laterality of several types of low frequency bandpass stimuli with interaural time delays and or phase shifts including bandpass noise amplitude modulated stimuli with time delayed envelopes and bandpass filtered clicks this model is compared to other theories that describe lateralization in terms of the relative contributions of information in the envelopes and fine structures of binaural stimuli

contribution of harmonicity and location to auditory object formation in free field evidence from event related brain potentials the contribution of location and harmonicity cues in sound segregation was investigated using behavioral reports and source waveforms derived from the scalp recorded evoked potentials participants were presented with sounds composed of multiple harmonics in a free field environment the third harmonic was either tuned or mistuned and could be presented from the same or different location from the remaining harmonics presenting the third harmonic at a different location than the remaining harmonics increased the likelihood of hearing the tuned or slightly i e 2 mistuned harmonic as a separate object partials mistuned by 16 of their original value pop out of the complex and were paralleled by an object related negativity orn that superimposed the n1 and p2 components for the 2 mistuned stimuli the orn was present only when the mistuned harmonic was presented at a different location than the remaining harmonics presenting the tuned harmonic at a different location also yielded changes in neural activity between 150 and 250 ms after sound onset the behavioral and electrophysiological results indicate that listeners can segregate sounds based on harmonicity or location alone the results also indicate that a conjunction of harmonicity and location cues contribute to sound segregation primarily when harmonicity is ambiguous

the combination of interaural information across frequencies lateralization on the basis of interaural delay three experiments were carried out that employed low frequency tone complexes with interaural delays that varied across the frequency domain in the first experiment threshold interaural delays were measured for three tone complexes for which one two or all three components were delayed the center frequency was 750 hz and the frequency spacing f between components was 20 50 100 250 or 450 hz for all f s the presence of two diotic components elevated the threshold interaural delays obtained for the third component relative to that obtained for a pure tone of the same frequency in the second experiment observers made left right judgments regarding the direction of movement of signals for which two components were delayed by 25 s to the left ear during one interval and to the right ear during the other interval while a third component of a variable time difference was delayed to the opposite side as the tone pair subjects reported single intracranial images during each interval and the data showed that interaural delays of one component to one ear could be offset by interaural delays of the other two components to the other ear in the final experiment threshold interaural delays were measured for five tone complexes in which one two three four or five components were delayed the center frequency was 750 hz and f was fixed at 100 hz thresholds decreased in a linear fashion as the number of delayed components increased falling by about a factor of 5 as the number of delayed components went from one to five these results are consistent with spectrally synthetic binaural processing with the lateral position of intracranial images determined by a combination of interaural information across the spectrum these effects could be brought about by a linear combination of the outputs of frequency specific cross correlation networks or by a wideband cross correlation of the signals at the two ears

parametric solutions to sylvester conjugate matrix equations by two recently proposed operations with respect to complex matrices a simple explicit solution to the sylvester conjugate matrix equation is given in a finite series form the obtained solution can also be equivalently expressed in terms of the so called controllability like matrix and observability like matrix the proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix an illustrative example is employed to show the effectiveness of the proposed method

the effects of randomizing values of interaural disparities on binaural detection and on discrimination of interaural correlation the purpose of this study was to assess whether randomizing roving baseline interaural parameters of binaural stimuli would adversely affect performance in masking level difference and in interaural correlation discrimination paradigms listeners detection thresholds were measured in noso and nos configurations for both broadband 100 3000 hz and narrow band 450 550 hz maskers centered at 500 hz in addition thresholds of interaural decorrelation from a reference correlation of 1 0 were measured for 100 hz wide bands of noise centered at 500 hz data were obtained under conditions in which either values of itd or values of iid were roved both within and across trials data were also collected in the absence of a rove the range of the rove was 500 s for itds and was 6 db for iids the duration of the stimuli was varied between 17 and 310 ms overall the results indicate that independent of duration roving the interaural cues produced small degradations of performance as compared to data ob

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

binaural interference in lateralization thresholds for interaural time and level differences listeners discriminated changes in either interaural time differences itds or interaural level differences ilds in one noise band the target in the presence or absence of an uninformative spectrally remote second noise band the interferer the noise bands had center frequencies of 500 and 4000 hz and bandwidths of 50 and 400 hz respectively when one band was a target the other served as an interferer the interferer was presented either diotically or dichotically with itds or ilds that varied randomly across intervals interference was defined as occurring if the target thresholds were elevated in the presence of an interferer for itd discrimination interference was greater for the 4000 hz target than for the 500 hz target but for ild discrimination interference for the 500 hz target was greater than or equal to that obtained for the 4000 hz target larger interference effects were obtained when the interferer itd or ild was randomly varied revealing that interference can be large not only for high frequency targets but also for low frequency targets with high frequency interferers the data are consistent with a model in which listeners combine lateral position across frequency with interaural information weighted according to the accuracy with which positions are encoded in each frequency region

double hopf bifurcation for van der pol duffing oscillator with parametric delay feedback control the stability and bifurcation of a van der pol duffing oscillator with the delay feedback are investigated in which the strength of feedback control is a nonlinear function of delay a geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and hopf bifurcations the hopf bifurcation curves and multi stable regions are obtained as two parameters vary some weak resonant and non resonant double hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the death island regions simultaneously by applying the center manifold theory the normal forms near the double hopf bifurcation points as well as classifications of local dynamics are analyzed furthermore some quasi periodic and chaotic motions are verified in both theoretical and numerical ways

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

van der pol s oscillator under delayed feedback the effect of delayed feedback on oscillatory behaviour is investigated for the classical van der pol oscillator it is shown how the presence of delay can change the amplitude of limit cycle oscillations or suppress them altogether the result is compared to the conventional proportional and derivative feedback the derivative like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping

on closed form solutions to the generalized sylvester conjugate matrix equation abstract in this paper several explicit parametric solutions to the generalized sylvester conjugate matrix equation are given the proposed solutions can provide all the degrees of freedom which are represented by a free parameter matrix in addition the approaches adopted in this paper do not require that the coefficient matrices are in any canonical forms

why do transposed stimuli enhance binaural processing interaural envelope correlation vs envelope normalized fourth moment high frequency transposed stimuli have been shown to yield enhanced processing of ongoing interaural temporal disparities itds this paper concerns determining which aspect or aspects of the envelopes of such stimuli mediate enhanced resolution of itd behavioral measures and quantitative analyses utilizing special classes of transposed stimuli show that the internal interaural envelope correlation accounts both qualitatively and quantitatively for the enhancement in contrast the normalized fourth moment of the envelope y which provides an index of the degree to which the envelopes of high frequency stimuli fluctuate does not lead to a successful accounting of the data

localization of sound in rooms v binaural coherence and human sensitivity to interaural time differences in noise binaural recordings of noise in rooms were used to determine the relationship between binaural coherence and the effectiveness of the interaural time difference itd as a cue for human sound localization experiments showed a strong monotonic relationship between the coherence and a listener s ability to discriminate values of itd the relationship was found to be independent of other widely varying acoustical properties of the rooms however the relationship varied dramatically with noise band center frequency the ability to discriminate small itd changes was greatest for a mid frequency band to achieve sensitivity comparable to mid band the binaural coherence had to be much larger at high frequency where waveform itd cues are imperceptible and also at low frequency where the binaural coherence in a room is necessarily large rivalry experiments with opposing interaural level differences ilds found that the trading ratio between itd and ild increasingly favored the ild as coherence decreased suggesting that the perceptual weight of the itd is decreased by increased reflections in rooms

oscillations in a van der pol equation with delayed argument we consider the van der pol equation d2dt2u t eddtu t eu2 t r ddtu t r u t 0 with the delayed time r where r and e are real parameters with e 0 small and 0 r 2 and prove the existence and stability of a periodic solution with period near 2 and amplitude near 2 cosr with these properties this solution is unique up to translations in time

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

the normalized interaural correlation accounting for nospi thresholds obtained with gaussian and low noise masking noise recently j acoust soc am 103 2578 2589 1998 and j acoust soc am 103 2573 2577 1998 independently reported that greater masking of interaurally phase reversed s tones was produced by diotic low noise noise than by diotic gaussian noise based on quantitative analyses eddins and barber suggested that their results could not be accounted for by assuming that listeners judgments were based on constant criterion changes in the normalized interaural correlation produced by adding the s signal to the diotic masker in particular they showed that a model like the one previously employed by j acoust soc am 100 3774 3784 1996 predicted an ordering of thresholds between the conditions of interest that was opposite to that observed bernstein and trahiotis computed the normalized interaural correlation subsequent to half wave square law rectification and low pass filtering the parameters of which were chosen to mimic peripheral auditory processing in this report it is demonstrat

stability and bifurcation analysis in van der pol s oscillator with delayed feedback abstract the classical van der pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered linear stability of the equations is investigated by analyzing the associated characteristic equations it is found that there exist the stability switches when delay varies and the hopf bifurcation occurs when the delay passes through a sequence of critical values the bifurcation diagram is drawn in e k plane and the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem

effects of sensorineural hearing loss on interaural discrimination and virtual localization cross frequency binaural processing was investigated in listeners with normal hearing nh and with bilateral high frequency sensorineural hearing impairment ih in experiment 1 just noticeable differences for interaural time and interaural intensity were measured using 1 3 octave narrow band noises nbns centered at 0 5 and 4 khz these stimuli were presented in isolation and in different cross frequency interaural combinations ih listeners displayed the best interaural time discrimination when the 0 5 khz nbn was dichotic and the best intensity discrimination when both bands were dichotic both nh listeners time and ih listeners time and intensity displayed the poorest interaural discrimination when the nbns were presented simultaneously with interaural differences in only the 4 khz nbn 0 5 khz nbn dichotic localization accuracy was measured in experiment 2 using the 0 5 and 4 khz nbns in isolation and with 0 5 khz target 4 khz interferer and 4 khz target 0 5 khz interferer conditions best localization of nh and ih subjects was seen for the 0 5 khz target with or without an interferer poorest localization of ih subjects was observed for the 4 khz target and 0 5 khz interferer results suggest that for these ih subjects localization is most difficult when they are forced to rely on interaural information in a higher frequency region with conflicting interaural information at low frequencies

the role of envelope statistics in detecting changes in interaural correlation the role of envelope statistics in binaural masking level differences bmlds and correlation change detection was investigated in normal hearing listeners thresholds and just noticeable differences jnds were measured for different bandwidths and center frequencies 500 2000 4000 and 8000 hz using gaussian noises gns and low fluctuation noises lfns at a 500 hz center frequency gn noso thresholds were higher than nos thresholds were lower than and correlation change detection jnds were the same as lfn thresholds and jnds at higher center frequencies gn nos thresholds were the same or higher than lfn thresholds and gn correlation change detection jnds were much smaller than lfn jnds using a pulsed sine vocoder a second experiment was performed to investigate if binaural adaptation might contribute to the difference in gn and lfn detection there was no effect of pulse rate thus providing no clear evidence that binaural adaptation plays a role in these tasks both a cross correlation model and a model that utilized the fluctuations in the interaural differences could explain a majority of the variance in the lfn correlation change jnds

technical communique complete parametric approach for eigenstructure assignment in a class of second order linear systems this note deals with eigenstructure assignment in the second order linear system email protected email protected cq bu using the proportional plus derivative feedback controller u k 0q k email protected under the controllability condition of the matrix pair ab very simple general and complete parametric expressions in direct closed forms for both the closed loop eigenvector matrix and the feedback gains are established in terms of the closed loop eigenvalues and a group of parameter vectors the main computations are two sets of elementary matrix transformations which can be replaced by a series of singular value decompositions when the closed loop eigenvalues are chosen a priori the approach utilizes directly the original system data a b and c and involves manipulations on only n dimensional matrices an example illustrates the effect of the proposed approach

the influence of different segments of the ongoing envelope on sensitivity to interaural time delays the auditory system is sensitive to interaural timing disparities in the fine structure and the envelope of sounds each contributing important cues for lateralization in this study psychophysical measurements were conducted with customized envelope waveforms in order to investigate the isolated effect of different segments of a periodic ongoing envelope on lateralization one envelope cycle was composed of the four segments attack flank hold duration decay flank and pause duration which were independently varied to customize the envelope waveform the envelope waveforms were applied to a 4 khz sinusoidal carrier and just noticeable envelope interaural time differences were measured in six normal hearing subjects the results indicate that attack durations and pause durations prior to the attack are the most important stimulus characteristics for processing envelope timing disparities the results were compared to predictions of three binaural lateralization models based on the normalized cross correlation coefficient two of the models included an additional stage to mimic neural adaptation prior to binaural interaction involving either a single short time constant 5 ms or a combination of five time constants up to 500 ms it was shown that the model with the single short time constant accounted best for the data

a new block algorithm for full rank solution of the sylvester observer equation a new block algorithm for computing a full rank solution of the sylvester observer equation arising in state estimation is proposed the major computational kernels of this algorithm are 1 solutions of standard sylvester equations in each case of which one of the matrices is of much smaller order than that of the system matrix and furthermore this small matrix can be chosen arbitrarily and 2 orthogonal reduction of small order matrices there are numerically stable algorithms for performing these tasks including the krylov subspace methods for solving large and sparse sylvester equations the proposed algorithm is also rich in level 3 basic linear algebra subroutine blas 3 computations and is thus suitable for high performance computing furthermore the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

on the use of the normalized correlation as an index of interaural envelope correlation the purpose of the present study was to obtain new empirical observations that would help determine the form of interaural envelope correlation that accounts for listeners sensitivity to binaural information conveyed by high frequency stimuli in a four interval two alternative task listeners detected which interval contained a 4 khz tone added antiphasically to diotic 200 hz wide noise nos the nonsignal intervals contained the tone added homophasically noso discriminability d was measured as a function of s n for values between 30 and 30 db for all s ns overall level was 70 db spl using a similar procedure listeners were also tested in direct discrimination tasks where changes in envelope correlations were produced in one of two manners first changes in the normalized interaural envelope correlation were produced by varying the degree to which the envelopes covaried this was accomplished by mixing two independent gaussian noises second changes in the normalized interaural envelope correlation were produced by adding dc values to the envelopes of the stimuli overall in both experiments listeners ability to discriminate changes in interaural envelope correlation from a base correlation of 1 0 was well accounted for by the normalized correlation it is also shown that the normalized correlation of the envelope accounts for classic data concerning discriminability of interaural time differences at high frequencies as a function of depth of modulation

the combination of interaural information across frequencies the effects of number and spacing of components onset asynchrony and harmonicitya threshold interaural delays were measured for a single interaurally delayed low frequency target component presented against a background of two four six or eight diotic distractor components in the first experiment a 753 hz target and the flanking distractor components were gated on and off simultaneously in subsequent experiments the distractors were gated on 25 200 ms prior to the target in addition the target and distractor components were given various harmonic configurations in general threshold interaural delays were higher in all conditions in which distractors were present relative to thresholds obtained for the target component in isolation subjects reported that the pitch of the target component was more salient when an onset asynchrony between the target and distractors was present but the components were perceived as occupying a single intracranial position in spite of the various interaural delays across the frequency domain these results suggest that binaural processing of stimuli consisting of a small number of low frequency temporally overlapping components occurs in a spectrally synthetic manner in which interaural information is combined across the spectrum even in situations in which the segregation of pitch information occurs

hopf pitchfork bifurcation in van der pol s oscillator with nonlinear delayed feedback abstract first we identify the critical values for hopf pitchfork bifurcation second we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point by the normal form method and center manifold theory then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system furthermore we find some interesting phenomena such as the coexistence of two asymptotically stable states two stable periodic orbits and two attractive quasi periodic motions which are verified both theoretically and numerically

toroidal normal forms for bifurcations in retarded functional differential equations i multiple hopf and transcritical multiple hopf interaction abstract for finite dimensional bifurcation problems it is well known that it is possible to compute normal forms which possess nice symmetry properties oftentimes these symmetries may allow for a partial decoupling of the normal form into a so called radial part and an angular part analysis of the radial part usually gives an enormous amount of valuable information about the bifurcation and its unfoldings in this paper we are interested in the case where such bifurcations occur in retarded functional differential equations and we revisit the realizability and restrictions problem for the class of radial equations by nonlinear delay differential equations our analysis allows us to recover and considerably generalize recent results by faria and magalhaes t faria l t magalhaes restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities j dynam differential equations 8 1996 35 70 and by buono and belair p l buono j belair restrictions and unfolding of double hopf bifurcation in functional differential equations j differential equations 189 2003 234 266

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

closed form solutions to sylvester conjugate matrix equations some explicit closed form solutions of homogeneous and nonhomogeneous sylvester conjugate matrix equations are provided in this paper one of the solutions is expressed in terms of controllability matrices and observability matrices the proposed approach does not require all the coefficient matrices to be in any canonical forms and the solutions provide a significant degree of freedom which is represented by an arbitrarily chosen parameter matrix by specifying the solutions of the homogeneous sylvester conjugate equation some new expressions of the solutions of the normal sylvester normal sylvester conjugate and sylvester equations are given this fact reveals that the sylveter conjugate matrix equations are a more general class of some previously investigated matrix equations

formulation of the normal form of turing hopf bifurcation in partial functional differential equations abstract turing hopf bifurcation is considered as an important mechanism for generating complex spatio temporal patterns in dynamical systems in this work the normal form up to the third order for the hopf steady state bifurcation which includes the turing hopf bifurcation of a general system of partial functional differential equations pfdes in a bounded spatial region of any dimension is derived based on the center manifold and the normal form theories of pfdes the explicit formula for the coefficients in the normal form of hopf steady state bifurcation are presented concisely in a matrix form which makes it more convenient in not only symbolic derivation but also numerical implementation this provides an approach of showing the existence and stability of stationary and time periodic solutions with spatial heterogeneity the derived formulas are also applicable to partial differential equations and functional differential equations

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

binaural detection as a function of interaural correlation and bandwidth of masking noise implications for estimates of spectral resolution detection thresholds were measured for an antiphasic s 500 hz tone masked by a binaural noise as a function of the bandwidth of the noise several values of interaural correlation of the masking noise were used ranging from 1 to 1 the bandwidth dependence of the thresholds showed a pattern consistent with a 100 hz wide critical band for most values of interaural correlation even for those values which resulted in a considerable binaural release of masking only when the interaural correlation of the masking noise was very close to or equal to unity was the bandwidth dependence of the thresholds in accord with an approximately 300 hz wide binaural critical band measured in previous studies our analysis of the data calls into question the commonly stated notion that binaural processing is characterized by a wider critical band than is monaural processing

interaural correlation discrimination i bandwidth and level dependence measurements of interaural cross correlation jnds from two reference correlations at several bandwidths were obtained for constant total power and constant spectral power gaussian noise at a reference correlation of 1 the results indicate that for bandwidths less than or equal to 115 hz the jnd remains at a constant value of approximately 0 004 and monotonically increases discrimination performance degrades to approximately 0 04 as bandwidth increases above 115 hz at a reference correlation of 0 the jnd decreases discrimination performance improves from approximately 0 7 to 0 35 as the bandwidth increases from 3 to 115 hz and remains at a constant value of approximately 0 35 for bandwidths greater than 115 hz a decrease in the spectral level causes an increase in the jnds at a reference correlation of 1 and no change in the jnds at a reference correlation of 0 of the three models tested none is able to completely describe all of the empirical results

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

solution to matrix equation av bw evf and eigenstructure assignment for descriptor systems a simple complete analytical restriction free parametric solution with complete and explicit freedom of matrix equation av bw evf is presented based on the presented solution of this equation an approach for eigenstructure assignment for continuous descriptor system ex ax bu via descriptor variable feedback u kx is proposed parametric forms of the gain matrix and the eigenvectors associated with the assigned finite closed loop eigenvalues are given the approach is shown to be better than that of fahmy and o reilly 1989 int j contr 49 129 143 in the sense that it not only possesses the functions of the approach of fahmy and o reilly 1989 int j contr 49 129 143 but also has the following three advantages 1 it eliminates the requirements on the assigned finite closed loop poles 2 it provides more design parameters and 3 it needs less computational work

lateralization produced by interaural temporal and intensitive disparities of high frequency raised sine stimuli data and modeling an acoustic pointing task was used to measure extents of laterality produced by combinations of ongoing envelope based interaural temporal disparities itds and interaural intensitive disparities iids of 4 khz centered raised sine stimuli bernstein and trahiotis j acoust soc am 125 3234 3242 2009 while varying parametrically their peakedness depth of modulation and frequency of modulation the study was designed to assess whether iids act as weights within the putative binaural display at high spectral frequencies where the envelopes convey itd information as appears to be the case at low spectral frequencies where the waveforms i e fine structure and envelopes convey itd information the data indicate that envelope based iids do principally act as weights and that they appear to exert their influence on lateral position independently of the influence of itds quantitative analyses revealed that an augmented form of the cross correlation based position variable model of stern and shear j acoust soc am 100 2278 2288 1996 accounted for 94 of the variance in the data this success notwithstanding for a small subset of the data predictions could be improved by assuming that the listeners utilized information within auditory filters having center frequencies above 4 khz

comparing the effect of pause duration on threshold interaural time differences between exponential and squared sine envelopes l recently two studies klein hennig et al j acoust soc am 129 3856 3872 2011 laback et al j acoust soc am 130 1515 1529 2011 independently investigated the isolated effect of pause duration on sensitivity to interaural time differences itd in the ongoing stimulus envelope the steepness of the threshold itd as a function of pause duration functions differed considerably across studies the present study using matched carrier and modulation frequencies directly compared threshold itds for the two envelope flank shapes from those studies the results agree well when defining the metric of pause duration based on modulation depth sensitivity

discrimination of interaural temporal disparities by normal hearing listeners and listeners with high frequency sensorineural hearing loss thresholds of ongoing interaural time difference itd were obtained from normal hearing and hearing impaired listeners who had high frequency sensorineural hearing loss several stimuli a 500 hz sinusoid a narrow band noise centered at 500 hz a sinusoidally amplitude modulated 4000 hz tone and a narrow band noise centered at 4000 hz and two criteria equal sound pressure level eq spl and equal sensation level eq sl for determining the level of stimuli presented to each listener were employed the itd thresholds and slopes of the psychometric functions were elevated for hearing impaired listeners for the two high frequency stimuli in comparison to a the listener s own low frequency thresholds and b data obtained from normal hearing listeners for stimuli presented with eq spl interaurally the two groups of listeners required similar itds to reach threshold when stimuli were presented at eq sls to each ear for low frequency stimuli the itd thresholds of the hearing impaired listener were

iterative solutions to coupled sylvester conjugate matrix equations this paper is concerned with iterative solutions to the coupled sylvester conjugate matrix equation with a unique solution by applying a hierarchical identification principle an iterative algorithm is established to solve this class of complex matrix equations with a real representation of a complex matrix as a tool a sufficient condition is given to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices in addition a sufficient convergence condition that is easier to compute is also given by the original coefficient matrices finally a numerical example is given to verify the effectiveness of the proposed algorithm

saddle node hopf bifurcation in a modified leslie gower predator prey model with time delay and prey harvesting abstract from the saddle node hopf bifurcation point of view this paper considers a modified leslie gower predator prey model with time delay and the michaelis menten type prey harvesting firstly we discuss the stability of the equilibria obtain the critical conditions for the saddle node hopf bifurcation and give the completion bifurcation set by calculating the universal unfoldings near the saddle node hopf bifurcation point by using the normal form theory and center manifold theorem then we derive the parameter conditions for the existence of monostable coexistence equilibrium and the parameter regions in which both the prey extinction and the coexistence equilibrium or coexistence periodic or quasi periodic solutions are simultaneously stabilized we also investigate the heteroclinic bifurcation and describe the phenomenon that the periodic behavior disappears as through the heteroclinic bifurcation finally some numerical simulations are performed to support our analytic results

qualitative analysis in a delayed van der pol oscillator abstract the main purpose of this manuscript is to introduce and compare two methods for discussing the nature of hopf bifurcation namely a research method combining the normal form theory and the center manifold theorem and the other method of multiple scales taking a delayed van der pol oscillator as an example the local stability as well as the occurrence of hopf bifurcation are explored via choosing time delay as the bifurcation parameter on the basis of two different methods respectively the characters of hopf bifurcation which includes the direction of hopf bifurcation as well as the stability of bifurcating periodic solutions are analyzed finally numerical simulations supporting the theoretical findings are given and it is observed that the results of two methods are consistent

enhancing interaural delay based extents of laterality at high frequencies by using transposed stimuli an acoustic pointing task was used to determine whether interaural temporal disparities itds conveyed by high frequency transposed stimuli would produce larger extents of laterality than itds conveyed by bands of high frequency gaussian noise the envelopes of transposed stimuli are designed to provide high frequency channels with information similar to that conveyed by the waveforms of low frequency stimuli lateralization was measured for low frequency gaussian noises the same noises transposed to 4 khz and high frequency gaussian bands of noise centered at 4 khz extents of laterality obtained with the transposed stimuli were greater than those obtained with bands of gaussian noise centered at 4 khz and in some cases were equivalent to those obtained with low frequency stimuli in a second experiment the general effects on lateral position produced by imposed combinations of bandwidth itd and interaural phase disparities ipds on low frequency stimuli remained when those stimuli were transposed to 4 khz overall the data were fairly well accounted for by a model that computes the cross correlation subsequent to known stages of peripheral auditory processing augmented by low pass filtering of the envelopes within the high frequency channels of each ear

solutions to a family of matrix equations by using the kronecker matrix polynomials closed form solutions to a family of generalized sylvester matrix equation in form of i 0 fa ixf email protected i 0 jb kyf email protected j 0 fe jrf j are given by using the so called kronecker matrix polynomials it is found that the structure of the solutions is independent of the orders f j and f this type of uniform closed form solutions includes our early results as special cases the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in linear systems

on solving the lyapunov and stein equations for a companion matrix when the matrix a is in companion form the essential step in solving the lyapunov equation pa atp q involves a linear n n system for the first column of the solution matrix p the complex dependence on the data matrices a and q renders this system unsuitable for actual computation in this paper we derive an equivalent system which exhibits simpler dependence on a and q as well as improved complexity and robustness characteristics a similar results is obtained also for the stein equation p atpa q

the explicit solutions and solvability of linear matrix equations abstract by factorizations and the smith normal form of polynomial matrix this paper discusses the explicit solution and solvability of the linear matrix equation i 0 k a i xb i c over a field

lateralization produced by envelope based interaural temporal disparities of high frequency raised sine stimuli empirical data and modeling an acoustic pointing task was used to measure extents of laterality produced by ongoing interaural temporal disparities itds conveyed by the envelopes of 4 khz centered raised sine stimuli while varying parametrically their peakedness depth of modulation and frequency of modulation one purpose of the study was to determine whether such manipulations would produce changes in laterality logically consistent with those found for itd discrimination thresholds reported by bernstein and trahiotis j acoust soc am 125 3234 3242 2009 the data obtained revealed that they did in that 1 increasing depth of modulation peakedness or frequency of modulation between 32 and 128 hz produced smaller threshold itds and greater laterality and 2 increasing frequency of modulation to 256 hz produced modest increases in threshold itds and modest decreases in laterality the extents of laterality measured were successfully accounted for via an augmentation of the cross correlation based position variable modeling approach developed by stern and shear j acoust soc am 100 2278 2288 1996 to account for itd based extents of laterality obtained at low spectral frequencies

the lateralization of simple dichotic pitches a simple dichotic pitch arises when a single narrow band possesses a different interaural configuration from a surrounding broadband noise whose interaural configuration is uniform and correlated such pitches were created by interaurally decorrelating a narrow band experiment 1 or by giving a narrow band a different interaural time difference from the noise experiment 2 using an adaptive forced choice procedure listeners adjusted the interaural intensity difference of pointers to match their lateralization to that of the dichotic pitches the primary determinants of lateralization were the interaural configuration of the broadband noise experiment 1 the center frequency of the narrow band experiment 1 and its interaural configuration experiment 2 the ability of two computational models to predict these results was evaluated a version of the central spectrum model j raatgever and f a bilsen j acoust soc am 80 429 441 1986 incorporating realistic frequency selectivity accounted for the main results of experiment 1 but not experiment 2 a new reconstruction comparison model accounted for the main results of both experiments to accommodate the variables shown to influence lateralization this model segregates evidence of the dichotic pitch from the noise reconstructs the cross correlogram of the noise and compares it with the cross correlogram of the original stimulus

double hopf bifurcation and quasi periodic attractors in delay coupled limit cycle oscillators abstract we investigate the double hopf bifurcation at zero equilibrium point firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for delay coupled limit cycle oscillators and derive the universal unfolding and a complete bifurcation diagram of the system thirdly many interesting phenomena such as attractive periodic motion and three dimensional invariant torus are observed using numerical simulation finally the normal forms of several strong resonant cases are listed

normal forms for retarded functional differential equations and applications to bogdanov takens singularity abstract the paper addresses for retarded functional differential equations fdes the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity a phase space appropriate to the computation of these normal forms is introduced and adequate nonresonance conditions for the computation of the normal forms are derived as an application the general situation of bogdanov takens singularity and its versal unfolding for scalar retarded fdes with nondegeneracy at second order is considered both in the general case and in the case of differential delay equations of the form t x t x t 1

reduced order observers a new algorithm and proof this paper gives a new recursive algorithm to construct a reduced order observer with prescribed spectrum of a given observable system the method is based on the staircase form and implicitly gives a new proof for the existence of such reduced order observers

on a planar system modelling a neuron network with memory abstract we consider a delay differential equation modelling a network of two neurons with memory the situations without self connections and two delays and with self connections and two equal delays are addressed in terms of local stability and bifurcation analysis in the first case the dynamical behavior is studied by taking one of the delays as the bifurcating parameter namely the hopf bifurcation whose existence was proven in former works occurs as the delay crosses some critical values and is completely described conditions ensuring the stability of the periodic cycles are given when self connections are present hopf and pitchfork bifurcations co exist and the equation describing the flow on the center manifold is derived

iterative solutions to the kalman yakubovich conjugate matrix equation abstract two operations are introduced for complex matrices in terms of these two operations an infinite series expression is obtained for the unique solution of the kalman yakubovich conjugate matrix equation based on the obtained explicit solution some iterative algorithms are given for solving this class of matrix equations convergence properties of the proposed algorithms are also analyzed by using some properties of the proposed operations for complex matrices

spectral properties of sums of certain kronecker products we introduce two kinds of sums of kronecker products and their induced operators we study the algebraic properties of these two kinds of matrices and their associated operators the properties include their eigenvalues their eigenvectors and the relationships between their spectral radii or spectral abscissae furthermore two projected matrices of these kronecker products and their induced operators are also studied

stability and bifurcation analysis of micro electromechanical nonlinear coupling system with delay abstract in this paper we study dynamics in delayed micro electromechanical nonlinear coupling system with particular attention focused on hopf and hopf pitchfork bifurcations based on the distribution of eigenvalues we prove that a sequence of hopf and hopf pitchfork bifurcations occur at the trivial equilibrium as the delay increases and obtain the critical values of two types of bifurcations next by applying the multiple time scales method the normal forms near the hopf and hopf pitchfork bifurcations critical points are derived finally bifurcation analysis and numerical simulations are presented to demonstrate the application of the theoretical results we show the regions near above bifurcation critical points in which the micro electromechanical nonlinear coupling system exists stable fixed point or stable periodic solution detailed numerical analysis using matlab extends the local bifurcation analysis to a global picture and stable windows are observed as we change control parameters namely the stable fixed point and stable periodic solution can exist in large regions of unfolding parameters as the unfolding parameters increase away from the critical value

effects of level and background noise on interaural time difference discrimination for transposed stimuli just noticeable interaural time differences were measured for low frequency pure tones high frequency sinusoidally amplitude modulated sam tones and high frequency transposed stimuli at multiple levels with or without a spectrally notched diotic noise to prevent spread of excitation performance with transposed stimuli and pure tones was similar in quiet however in noise performance was poorer for transposed stimuli than for pure tones performance with sam tones was always poorest in all conditions performance improved slightly with increasing level the results suggest that the equivalence postulated between transposed stimuli and pure tones is not valid in the presence of a spectrally notched background noise

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

constraint generalized sylvester matrix equations in this paper some necessary and sufficient conditions are established for the constraint generalized sylvester matrix equations to have a common solution the expression of the general common solution is also given under the solvable conditions in addition a numerical example is presented to illustrate the presented theory

perceptual fusion and fragmentation of complex tones made inharmonic by applying different degrees of frequency shift and spectral stretch global pitch depends on harmonic relations between components but the perceptual coherence of a complex tone cannot be explained in the same way instead it has been proposed that the auditory system responds to a common pattern of equal spacing between components but is only sensitive to deviations from this pattern over a limited range roberts and brunstrom j acoust soc am 104 2326 2338 1998 this hypothesis predicts that spectral fusion will be largely unaffected either by frequency shifting a harmonic stimulus because equal spacing is preserved or by small degrees of spectral stretch because significant deviations from equal spacing only cumulate over large spectral distances complex tones were either shifted by 0 50 of f0 200 hz 10 or stretched by 0 12 of f0 100 hz 10 subjects heard a complex followed by a pure tone in a continuous loop one of the components 2 11 was mistuned by 4 and subjects adjusted the pure tone to match its pitch broadly consistent with our hypothesis frequency shifts had relatively little effect on hit rates and only large degrees of stretch reduced them substantially the implications for simultaneous grouping are explored with reference to an autocorrelation model of auditory processing

oscillation sliding in a modified van der pol duffing electronic oscillator abstract some periodic behaviour exhibited by a modified van der pol duffing electronic oscillator near a degenerate hopf pitchfork bifurcation have been studied numerical continuation of these periodic orbits leads to the appearance of interesting phenomena after varying one of the characteristics of the oscillator oscillation sliding between two periodic regimes is detected in the region where oscillation sliding is present quasiperiodic oscillations invariant torus breakdown of the torus and the corresponding resonant periodic orbits are also found

kronecker maps and sylvester polynomial matrix equations the concepts of kronecker maps and sylvester polynomial matrix equations are proposed some properties of the kronecker maps are deduced it is shown that many kinds of matrix equations can be formulated into the so called sylvester polynomial matrix equations with the help of the kronecker maps general explicit solutions of the sylvester polynomial matrix equations are established when the polynomial matrices possess f primeness for the nonsquare case the proposed solutions can offer all the degrees of freedom represented by a free parameter matrix

a faddeev sequence method for solving lyapunov and sylvester equations lyapunov and sylvester equations play an important role in linear systems theory this paper deals with a method of solving such equations of the form ap pb k and p apb k with a rm m b rn n and p k rm n by exploiting the matrix algebra structure of the problem no use is made of kronecker products and the largest matrices occurring in the algorithms are of sizes m m n n and m n the faddeev method for matrix inversion lies at the very heart of the algorithms presented it occurs on several levels of the problem for the matrices a and b and for the lyapunov and sylvester operators the resulting algorithms are capable of solving the equations in a finite number of recursion steps they are very much apt for symbolic calculation it is shown how a solution can be quickly obtained for an equation with an arbitrary right hand side k provided a solution is known for a right hand side xyt of rank 1 where a x and bt y are reachable pairs the concept of a faddeev reachability matrix introduced here turns out to be very useful it establishes a close connection between the controller canonical companion form of a reachable pair a b and the faddeev sequence of a if a is already on controller form then its faddeev sequence takes on an especially simple form also in the symmetric case where a bt many important simplifications arise for this case alternative algorithms that require less iterations are developed the paper concludes with some examples concerning the symbolic solution of the lyapunov equation ap pat bbt with a b on controller form showing the potential of the algorithms

a complete analytical solution to the equation ta ft lc and its applications in this note a complete analytical and restriction free solution with complete and explicit freedom of the matrix equation ta ft lc is proposed here a c is given and is observable and f is in the jordan form with arbitrary given eigenvalues this solution appears to be new because it can be applied directly to obtain significantly better solutions to the following three basic design problems 1 2 d system eigenvalue assignment 2 function observer design and 3 state feedback eigenstructure design as shown in this note

the normalized correlation accounting for nosπ thresholds with gaussian and low noise masking noise recently both eddins and barber j acoust soc am 103 2578 2589 1998 and hall et al j acoust soc am 103 2573 2577 1998 demonstrated that low noise noise produced more masking of antipha sic tones than did gaussian noise eddins and barber could not account for this finding by considering changes in the normalized interaural correlation produced by adding antiphasic signals to the diotic maskers they calculated the normalized correlation subsequent to half wave square law rectification and low pass filtering that approach was used successfully by bernstein and trahiotis j acoust soc am 100 3774 3784 1996 to account for binaural detection performance as a function of frequency in this presentation it will be shown that one can account quantitatively for thresholds obtained with low noise noise and with gaussian noise by incorporating a stage of compression prior to rectification and low pass filtering the compressive function employed produces effects similar to tho

effects of time delayed position feedback on a van der pol duffing oscillator abstract the mechanism for the action of time delay in a non autonomous system is investigated in this paper the original mathematical model under consideration is a van der pol duffing oscillator with excitation a delayed system is obtained by adding both linear and nonlinear time delayed position feedbacks to the original system functional analysis is used to change the delayed system into a functional differential equation fde the time delay is taken as a variable parameter to investigate its effect on the dynamics of the system such as the stability and bifurcation of an equilibrium point phase locked periodic and phase shifting solution period doubling quasi periodic motion and chaos a periodic solution expressed in the closed form with the aid of the center manifold and averaging theorem is found to be in good agreement with that obtained by numerical simulation two routes to chaos are found namely period doubling bifurcation and torus breaking the results obtained in this paper show that time delay may be used as a simple but efficient switch to control motions of a system either from order motion to chaos or from chaotic motion to order for different applications

accounting quantitatively for sensitivity to envelope based interaural temporal disparities at high frequencies bernstein and trahiotis 2009 j acoust soc am 125 3234 3242 reported threshold interaural temporal disparities itds conveyed by the envelopes of 4 khz centered raised sine stimuli a raised sine stimulus consists of a carrier modulated by a sinusoid raised to an exponent such stimuli permitted bernstein and trahiotis to vary independently stimulus modulation frequency modulation depth and relative peakedness deadtime an interaural correlation based model that included stages mimicking peripheral auditory processing captured most of the data save for an overestimation of threshold itds obtained when the depth of modulation was 25 and the raised sine exponent was 8 0 the purpose of the present study was 1 to present a quantitative evaluation of how well other measures including normalized envelope fourth moment envelope peakwidth and envelope deadtime might also account for the data reported by bernstein and trahiotis and 2 to present new threshold itds measured while varying factorially depth of modulation raised sine exponent and modulation frequency quantitative analyses of both the prior and the new data showed that the normalized interaural correlation computed subsequent to peripheral auditory processing provided the most accurate predictions importantly the overestimation of threshold itds did not occur when it was assumed that listeners can employ information within off frequency auditory filters

bogdanov takens singularity in van der pol s oscillator with delayed feedback abstract in this paper we study the classical van der pol s equation with delayed feedback we investigate the bogdanov takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state

manipulating the straightness and curvature of patterns of interaural cross correlation affects listeners sensitivity to changes in interaural delay the purpose of this study was to test the hypothesis that stimuli characterized by straight trajectories of their patterns of cross correlation foster greater sensitivity to changes in interaural temporal disparities itds than do stimuli characterized by more curved trajectories of their patterns of cross correlation to do so sensitivity to changes in itd was measured as a function of duration using a set of reference stimuli that yielded differing relative amounts of straightness within their patterns of cross correlation while keeping the dominant trajectory at or near midline the relative amounts of straightness were manipulated by employing specific combinations of bandwidth itd and interaural phase disparity ipd of gaussian noises centered at 500 hz the results were consistent with expectations in that the patterning of the threshold itds revealed increasingly poorer sensitivity as greater and greater curvature was imposed on the dominant midline trajectory the variations in threshold itd across the stimulus conditions can be accounted for quite well quantitatively by assuming either that the listeners based their judgments on changes in the position of the most central peak of the cross correlation function or that they based their judgments on changes in the centroid of a second level cross correlation function in a second experiment binaural detection was measured using a subset of the reference stimuli as maskers as expected sensitivity was poorest with the maskers characterized by the greatest curvature which were also those having the lowest interaural correlation

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

controllability observability and the solution of ax xb c a closed form finite series representation of the unique solution x of the matrix equation ax xb c is developed using this representation the image kernel and rank of x are related to the controllable and unobservable subspaces of the a c and c b pairs respectively bounds on the rank of x are obtainedin terms of the dimensions of these subspaces in the case that c has unitary rank an exact calculation of rank x is made the generic rank of x with a b fixed and c generic is evaluated

measures of extents of laterality for high frequency transposed stimuli under conditions of binaural interference our purpose in this study was to determine whether across frequency binaural interference would occur if itd based extents of laterality were measured using high frequency transposed stimuli as targets the results of an earlier study l r bernstein and c trahiotis j acoust soc am 116 3062 3069 2004 which focused on threshold itds rather than extents of laterality suggested that high frequency transposed stimuli might be immune to binaural interference effects resulting from the addition of a spectrally remote low frequency interferer in contrast to the earlier findings the data from this study indicate that high frequency transposed targets are susceptible to binaural interference nevertheless high frequency transposed targets even when presented along with an interferer yielded greater extents of itd based laterality than did high frequency gaussian noise targets presented in isolation that is the enhanced potency of itds conveyed by transposed stimuli persisted even in the