bifurcations of subharmonic solutions in reversible systems soit f r r n r r n une application c periodique cut on dit que l equation differentielle x f t x est reversible s il existe un operateur symetrique s sur r n tel que s 2 i de telles equations differentielles sont aussi appelees systemes avec la propriete e par rapport a s on etudie les bifurcations des solutions sous harmoniques de tels systemes reversibles

on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

infinite period bifurcation and global bifurcation branches branches of periodic solutions which exhibit the alternatives of the global hopf bifurcation theorem are calculated for two general systems of differential equations in the first a branch of solu

optimal linear estimation fusion i unified fusion rules this paper deals with data or information fusion for the purpose of estimation three estimation fusion architectures are considered centralized distributed and hybrid a unified linear model and a general framework for these three architectures are established optimal fusion rules based on the best linear unbiased estimation blue the weighted least squares wls and their generalized versions are presented for cases with complete incomplete or no prior information these rules are more general and flexible and have wider applicability than previous results for example they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time they are also in explicit forms convenient for implementation the optimal fusion rules presented are not limited to linear data models illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete incomplete or no prior information

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

on the track to track correlation problem the testing of the hypothesis whether two tracks represent the same target is considered previous works in the literature assumed that the estimates of the same target s state from two track files are uncorrelated a test that includes their correlation is presented

long range dependencies in heart rate signals revisited abstract the arguments are given that local exponents obtained in multifractal analysis by two methods wavelet transform modulus maxima wtmm and multifractal detrended fluctuation analysis mdfa allow to separate statistically hearts of healthy people and subjects suffering from reduced left ventricle systolic function nyha i iii class proposed indices of fractality suggest that a signal of human heart rate is a mixture of two processes monofractal and multifractal ones

decomposable principal component analysis in this paper we consider principal component analysis pca in decomposable gaussian graphical models we exploit the prior information in these models in order to distribute pca computation for this purpose we reformulate the pca problem in the sparse inverse covariance concentration domain and address the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph we illustrate our methodology in the context of decentralized anomaly detection in the abilene backbone network based on the topology of the network we propose an approximate statistical graphical model and distribute the computation of pca

bifurcation in classical bipolar transistor oscillator circuits the results of a systematic asymptotic analysis of two classical oscillator circuits are presented in this paper both circuits are composed of passive components and a single bipolar transistor they are each described by a third order system of nonlinear ordinary differential equations that is singularly perturbed in the limit varepsilon to 0 here varepsilon is the inverse of the circuit s q the two timing method is used to construct the asymptotic behavior of the solutions as varepsilon to 0 these solutions are shown to depend upon amplitudes that evolve on a slow time scale according to amplitude equations these amplitude equations are analyzed and the results are physically interpreted

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia human heart rate variability in the form of time series of intervals between heart beats shows complex fractal properties recently it was demonstrated many times that the fractal properties vary from point to point along the series leading to multifractality in this paper we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured this time scale is related to the frequency band of the signal we find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale we introduce a method called multiscale multifractal analysis mma which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale or frequency band mma is relatively immune to additive noise and nonstationarity including the nonstationarity due to inclusions into the time series of events of a different dynamics e g arrhythmic events in sinus rhythm the mma method may provide new ways of measuring the nonlinearity of a signal and it may help to develop new methods of medical diagnostics

multiscale multifractal time irreversibility analysis of stock markets abstract time irreversibility is one of the most important properties of nonstationary time series complex time series often demonstrate even multiscale time irreversibility such that not only the original but also coarse grained time series are asymmetric over a wide range of scales we study the multiscale time irreversibility of time series in this paper we develop a method called multiscale multifractal time irreversibility analysis mmra which allows us to extend the description of time irreversibility to include the dependence on the segment size and statistical moments we test the effectiveness of mmra in detecting multifractality and time irreversibility of time series generated from delayed henon map and binomial multifractal model then we employ our method to the time irreversibility analysis of stock markets in different regions we find that the emerging market has higher multifractality degree and time irreversibility compared with developed markets in this sense the mmra method may provide new angles in assessing the evolution stage of stock markets

audio visual group recognition using diffusion maps data fusion is a natural and common approach to recovering the state of physical systems but the dissimilar appearance of different sensors remains a fundamental obstacle we propose a unified embedding scheme for multisensory data based on the spectral diffusion framework which addresses this issue our scheme is purely data driven and assumes no a priori statistical or deterministic models of the data sources to extract the underlying structure we first embed separately each input channel the resultant structures are then combined in diffusion coordinates in particular as different sensors sample similar phenomena with different sampling densities we apply the density invariant laplace beltrami embedding this is a fundamental issue in multisensor acquisition and processing overlooked in prior approaches we extend previous work on group recognition and suggest a novel approach to the selection of diffusion coordinates to verify our approach we demonstrate performance improvements in audio visual speech recognition

merging of resonance tongues abstract this paper considers the resonance behavior found near a saddle node hopf bifurcation in a flow the global structure of resonance tongues is examined and it is shown that in the absence of certain symmetries different resonance tongues can merge with one another the position and shape of the resonance tongues are seen to be related to the presence of homoclinic and heteroclinic bifurcations of two saddle foci the implications of these results for the normal form analysis of the saddle node hopf bifurcation are discussed

sensor centric data reduction for estimation with wsns via censoring and quantization consider a wireless sensor network wsn with a fusion center fc deployed to estimate signal parameters from noisy sensor measurements if the wsn has a large number of low cost battery operated sensor nodes with limited transmission bandwidth then conservation of transmission resources power and bandwidth is paramount to this end the present paper develops a novel data reduction method which requires no inter sensor collaboration and results in only a subset of the sensor measurements transmitted to the fc using interval censoring as a data reduction method each sensor decides separately whether to censor its acquired measurements based on a rule that promotes censoring of measurements with least impact on the estimator mean square error mse leveraging the statistical distribution of sensor data the censoring mechanism and the received uncensored data fc based estimators are derived for both deterministic via maximum likelihood estimation and random parameters via maximum a posteriori probability estimation for a linear gaussian model quantization of the uncensored measurements at the sensor nodes offers an additional degree of freedom in the resource conservation versus estimator mse reduction tradeoff cramer rao bound analysis for the different censor estimators and censor quantizer estimators is also provided to benchmark and facilitate mse based performance comparisons numerical simulations corroborate the analytical findings and demonstrate that the proposed censoring estimation approach performs competitively with alternative methods under different sensing conditions while having lower computational complexity

data fusion with minimal communication two sensors obtain data vectors x and y respectively and transmit real vectors m spl i oarr sub 1 x and m spl i oarr sub 2 y respectively to a fusion center the authors obtain tight lower bounds on the number of messages the sum of the dimensions of m spl i oarr sub 1 and m spl i oarr sub 2 that have to be transmitted for the fusion center to be able to evaluate a given function f spl i oarr x y when the function f spl i oarr is linear they show that these bounds are effectively computable certain decentralized estimation problems can be cast in the framework and are discussed in some detail in particular the authors consider the case where x and y are random variables representing noisy measurements and f spl i oarr x y e z x y where z is a random variable to be estimated furthermore it is established that a standard method for combining decentralized estimates of gaussian random variables has nearly optimal communication requirements

sensors optimal dimensionality compression matrix in estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally pre compress sensor outputs sensor observations or estimates before sensors transmission to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion this paper will give an analytic solution of the optimal linear dimensionality compression matrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case as well as how to implement a gauss seidel algorithm to search for an optimal solution to linear dimensionality compression matrix

hyperplane based vector quantization for distributed estimation in wireless sensor networks this paper considers distributed estimation of a vector parameter in the presence of zero mean additive multivariate gaussian noise in wireless sensor networks due to stringent power and bandwidth constraints vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information which is then forwarded to a fusion center where a final estimate of the vector parameter is obtained within such a context this paper focuses on a class of hyperplane based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization it is shown that the key of the vector quantization design is to find a compression vector for each sensor under the framework of the cramer rao bound crb analysis the compression vector design problem is formulated as an optimization problem that minimizes the trace of the crb matrix such an optimization problem is extensively studied in particular an efficient iterative algorithm is developed for the general case along with optimal and near optimal solutions for some specific but important noise scenarios performance analysis and simulation results are carried out to illustrate the effectiveness of the proposed scheme

optimal dimensionality reduction of sensor data in multisensor estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally precompress sensor outputs sensor observations or estimates before the sensors transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion or when an allowed performance loss constraint exists one needs to design the minimum dimension of sensor data this paper will answer the above questions by using the matrix decomposition pseudo inverse and eigenvalue techniques

reduced dimension linear transform coding of correlated signals in networks a model called the linear transform network ltn is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs dags an ltn is a dag network with multiple source and receiver nodes source nodes transmit subspace projections of random correlated signals by applying reduced dimension linear transforms the subspace projections are linearly processed by multiple relays and routed to intended receivers each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error mse distortion the model is extended to include noisy networks with power constraints on transmitters a key task is to compute all local compression matrices and linear estimators in the network to minimize end to end distortion the nonconvex problem is solved iteratively within an optimization framework using constrained quadratic programs qps the proposed algorithm recovers as special cases the regular and distributed karhunen loeve transforms klts cut set lower bounds on the distortion region of multi source multi receiver networks are given for linear coding based on convex relaxations cut set lower bounds are also given for any coding strategy based on information theory the distortion region and compression estimation tradeoffs are illustrated for different communication demands e g multiple unicast and graph structures

optimum compression of a noisy measurement for transmission over a noisy channel this paper is motivated by sensing and wireless communication where data compression or dimension reduction may be used to reduce the required communication bandwidth high dimensional measurements are converted into low dimensional representations through linear compression our aim is to compress a noisy sensor measurement allowing for the fact that the compressed measurement will then be transmitted over a noisy channel we give the closed form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix we show that the solutions share a common architecture consisting of a canonical coordinate transformation scaling by coefficients which account for canonical correlations and channel noise variance followed by a coordinate transformation into the sub dominant invariant subspace of the channel noise furthermore we explore the design problem with respect to more general criteria and provide a unified factorization for the corresponding optimal compression matrix a necessary condition is obtained for the optimal compression

performance of multifractal detrended fluctuation analysis on short time series the performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono and multifractal models the reconstruction of the generalized hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series as an application the series of the daily exchange rate between the us dollar and the euro is studied sets with known fractal and multifractal behavior the results are applied to the analysis of the daily exchange rate between the us dollar and the euro this time se ries is relatively short around 3500 entries given that the euro currency debuted at the beginning of 1999 further more in its short life the euro has gone through a dubita tive start followed by a strong couple of years and since around 2008 it has been immersed in a crisis which has threatened its existence this turbulent history makes it interesting to ask if its dynamics have changed with time the paper is organized as follows in the next section the mfdfa method is briefly described and the notation used in the rest of the paper is introduced section iii presents the analysis of the mono and multifractal syn thetic data section iv discusses the application of the results to a time series from finance namely the daily ex change rate between the us dollar and the euro finally the conclusions of this work are presented in section v

quantifying sound field diffuseness in small rooms using multifractals with the aim of quantifying sound field uniformity in spaces of relatively low volume four different configurations in terms of acoustic treatment and sound field diffuseness were constructed and tested in a diffuse sound field reflections are not strongly correlated both to the original sound and to earlier reflections the degree of correlation is embedded in the impulse response structure but is not trivial to identify the room impulse responses exhibit self similarity and therefore may be treated as multifractal signals characterized by a singularity spectrum the singularity spectrum contains a wealth of information about the acoustic field established in the room the width of the singularity spectrum in particular is directly related to the complexity of the impulse response structure the uniformity of the sound field in the room can be evaluated by examining the variation of the singularity spectra with position a new definition for sound field diffuseness is given that is not based on the concept of the energy density the proposed method is simple to apply statistically robust and provides a measure of diffusion independent of the room reverberation

distributed adaptive quantization for wireless sensor networks from delta modulation to maximum likelihood we consider distributed parameter estimation using quantized observations in wireless sensor networks wsns where due to bandwidth constraint each sensor quantizes its local observation into one bit of information a conventional fixed quantization fq approach which employs a fixed threshold for all sensors incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated to address this difficulty we propose a distributed adaptive quantization aq approach which with sensors sequentially broadcasting their quantized data allows each sensor to adaptively adjust its quantization threshold three aq schemes are presented 1 aq fs that involves distributed delta modulation dm with a fixed stepsize 2 aq vs that employs dm with a variable stepsize and 3 aq ml that adjusts the threshold through a maximum likelihood ml estimation process the ml estimators associated with the three aq schemes are developed and their corresponding cramer rao bounds crbs are analyzed we show that our 1 bit aq approach is asymptotically optimum yielding an asymptotic crb that is only pi 2 times that of the clairvoyant sample mean estimator using unquantized observations

critical scale invariance in a healthy human heart rate we demonstrate the robust scale invariance in the probability density function pdf of detrended healthy human heart rate increments which is preserved not only in a quiescent condition but also in a dynamic state where the mean level of the heart rate is dramatically changing this scale independent and fractal structure is markedly different from the scale dependent pdf evolution observed in a turbulentlike cascade heart rate model these results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

rotating thermal convection neosteady and neoperiodic solutions this paper considers the secondary and cascading bifurcation of two dimensional steady and period thermal convection states in a rotating box previously developed asymptotic and perturbation methods that rely on the coalescence of two steady convection primary bifurcation points of the conduction state as the taylor number approaches a critical value are employed a multitime analysis is employed to construct asymptotic expansions of the solutions of the initial boundary value problem for the boussinesq theory the small parameter in the expansion is proportional to the deviation of the taylor number from its critical value to leading order the asymptotic expansion of the solution involves the mode amplitudes of the two interacting steady convection states the asymptotic analysis yields a first order system of two coupled ordinary differential equations for the slow time evolution of these amplitudes we investigate the steady states of these amplitude equations and their linearized stability these

multiscale aspects of cardiac control abstract we report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics we first review recent progress using wavelet based multifractal analysis magnitude and sign decomposition analysis and a new segmentation algorithm to quantify multiscale features of heartbeat interval series we then investigate how heartbeat dynamics change with circadian influences and under pathologic conditions and we discuss their possible relation to the underlaying cardiac control mechanisms the analytic tools we discuss may be used on a wider range of physiologic signals

robustness and perturbation in the modeled cascade heart rate variability in this study numerical experiments are conducted to examine the robustness of using cascade to describe the multifractal heart rate variability hrv by perturbing the hierarchical time scale structure and the multiplicative rule of the cascade it is shown that a rigid structure of the multiple time scales is not essential for the multifractal scaling in healthy hrv so long as there exists a tree structure for the multiplication to take place a multifractal hrv and related properties can be captured by using the cascade but the perturbation of the multiplicative rule can lead to a qualitative change in particular a multifractal to monofractal hrv transition can result after the product law is perturbed to an additive one at the fast time scale we suggest that this explains the similar hrv scaling transition in the parasympathetic nervous system blockade

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

bifurcations of mode equations spin waves abstract we study the bifurcations of the spin wave equations that describe the parametric pumping of collective modes in magnetic media we discuss the following dynamical phenomena i sequential excitation of modes via zero eigenvalue bifurcations ii hopf bifurcations followed or not by feigenbaum cascades of period doublings iii local and global homoclinic phenomena two new organizing centers for routes to chaos are identified in the classification given by guckenheimer and holmes one is the codimension two local bifurcation with one pair of imaginary eigenvalues and a zero eigenvalue to which many dynamical consequences are known the second global homoclinic bifurcations associated to splitting of separatrices in the limit where the system can be considered a hamiltonian subjected to weak dissipation and forcing

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

distributed state estimation with dimension reduction preprocessing system state estimation relies heavily on the measurements with the advance of sensing technology the ability to measure is no longer a bottleneck in many systems and more and more researchers now focus on the rich information setting i e big data however although information never hurts it does not help unconditionally how to make the most of it depends on whether we can process the data efficiently in some systems the inherent constraint such as the bandwidth and cost makes it necessary to reduce the dimension of the measurement before further processing the problem that the raw measurements are first preprocessed to reduce size and then used for estimation is addressed in this paper it is shown that there is a lower bound on the size of the preprocessed data such that if the size is beyond the bound there exists a closed form estimator design that the linear minimum mean square estimation can be obtained moreover we propose an algorithm that is guaranteed to converge to a stationary point to design an estimator in the conditions that the lower bound cannot be reached besides convergence the proposed algorithm guarantees bounded performance loss compared with the global optimal solution under some additional conditions finally simulation results in three different applications are shown to demonstrate the effectiveness of the proposed algorithm

hard and soft multifractal processes abstract we show that multifractal notions encompass a wider variety of phenomena than often believed ranked by increasing highest order of singularities we have geometric then microcanonical and finally canonical multifractals they are respectively localized and calm delocalized and calm and delocalized and wild canonical multifractals may also involve rare violent hard singularities which cause high order statistical moments to diverge we demonstrate this classification in the framework of universal multifractals characterized by three fundamental exponents

distributed fusion estimation with communication bandwidth constraints this technical note is concerned with the distributed kalman filtering problem for a class of networked multi sensor fusion systems nmfss with communication bandwidth constraints to satisfy finite communication bandwidth only partial components of the local vector estimation signals are transmitted to the fusion center fc at each time step where multiple binary variables are introduced to model this component transmitting process a novel compensation strategy is proposed to restructure the untransmitted components of each local estimate at the fc end and a recursive distributed fusion kalman filter dfkf is designed in the linear minimum variance sense moreover a simple suboptimal judgement criterion is proposed to determine a group of binary variables such that the mean square error of the designed dfkf is minimal at each time step an illustrative example is given to show the effectiveness of the proposed methods

distributed estimation using reduced dimensionality sensor observations we derive linear estimators of stationary random signals based on reduced dimensionality observations collected at distributed sensors and communicated to a fusion center over wireless links dimensionality reduction compresses sensor data to meet low power and bandwidth constraints while linearity in compression and estimation are well motivated by the limited computing capabilities wireless sensor networks are envisioned to operate with and by the desire to estimate random signals from observations with unknown probability density functions in the absence of fading and fusion center noise ideal links we cast this intertwined compression estimation problem in a canonical correlation analysis framework and derive closed form mean square error mse optimal estimators along with coordinate descent suboptimal alternatives that guarantee convergence at least to a stationary point likewise we develop estimators based on reduced dimensionality sensor observations in the presence of fading and additive noise at the fusion center nonideal links performance analysis and corroborating simulations demonstrate the merits of the novel distributed estimators relative to existing alternatives

interaction of steady and periodic bifurcating modes with imperfection effects in reaction diffusion systems asymptotic solutions for two dimensional reaction diffusion systems are obtained under suitable conditions a trivial solution independent of both time and space is assumed to exist and the linearized system about this solution is considered the analysis is restricted to the case where this linearized system possesses one real eigenvalue and a complex pair of eigenvalues all with real part approximately equal to zero steady periodic and doubly periodic bifurcating solutions are found with special attention given to the effects of imperfection in one of the parameters

nonlinear weighted measurement fusion unscented kalman filter with asymptotic optimality for the general nonlinear systems a universal weighted measurement fusion wmf algorithm is presented via the taylor series expansion method based on the proposed fusion algorithm and the well known unscented kalman filter ukf the wmf ukf is presented it is proven that the proposed wmf ukf asymptotically approaches to the centralized measurement fusion ukf cmf ukf with the increase of the order of taylor series expansion so it has the asymptotical global optimality we find that wmf ukf has less computational cost than the cmf ukf does with the increase of the number of sensors two examples are given to show the effectiveness of the proposed algorithms

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

multifractal estimates of monofractality in rr heart series in power spectrum ranges abstract two popular estimators of multifractal properties the wavelet transform modulus maxima method and multifractal detrended fluctuation analysis are applied to investigate signals consisting of normal rr series in 39 healthy subjects and 90 patients suffering from systolic dysfunction of the left ventricle however differently from standards for multifractal analysis the scaling is performed separately in intervals corresponding to standard power spectral bands low lf very low vlf and ultra low frequencies ulf tests on fractional brownian motions fbm are done to quantify properties of the estimators as detectors of monofractality in lf vlf and ulf bands arguments are given that multifractal analysis of rr series performed in these bands has a physiological meaning the increased activation of the sympathetic nervous system caused by heart disease is detected evidently only by analysis in lf the transition in multifractal characteristics between diurnal and nocturnal activity takes place when the analysis moves from lf and vlf to ulf only in ulf the diurnal heart rate variability can be approximated by fbm with a self similarity index of h 0 20

classification and unfoldings of 1 2 resonant hopf bifurcation in this paper we study the bifurcations of periodic solutions from an equilibrium point of a differential equation whose linearization has two pairs of simple pure imaginary complex conjugate eigenvalues which are in 1 2 ratio this corresponds to a hopf hopf mode interaction with 1 2 resonance as occurs in the context of dissipative mechanical systems using an approach based on liapunov schmidt reduction and singularity theory we give a framework in which to study these problems and their perturbations in two cases no distinguished parameter and one distinguished bifurcation parameter we give a complete classification of the generic cases and their unfoldings

sungular hopf bifurcation to relaxation oscillations this paper is a continuation of our study of singular hopf bifurcations to relaxation oscillations siam journal on applied mathematics 46 1986 pp 721 739 in our previous analysis a system of two first order nonlinear equatins is investigated and it is shown how the bifurcation problem can be reduced to a weakly perturbed conservative system of two first order equations in this paper a method based on analyzing nearly conservative quantities was developed to find the bifurcation diagram of the periodic solutions emerging from singular hopf bifurcation points specifically the subcritical hopf bifurcation of the fitzhugh nagumo equations is analyzed the extension from the earlier bifurcation analysis is achieved by performing a perturbation analysis from the first integral of the leading order nonlinear oscillator at a critical value of a parameter the first integral exists up to an additional order in the perturbed equation this condition permits the resolution of features determined by h

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected