adiabatic small noise fluctuations around anticipated synchronization a perspective from scalar master slave dynamics abstract in this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay langevin equations in this context we find necessary conditions that guarantee anticipated synchronization in the mean value fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics it is shown that external noise properties can be inferred by measuring this object conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found a detailed analysis of the dependence on the characteristic parameters is presented

scattering from an impedance object at the edge of a perfectly conducting wedge in this study scattering from impedance bodies positioned at the edge of a perfectly electrically conducting wedge is investigated in the treatment of the problem eigenfunction expansion in terms of spherical vector wave functions is employed a complete dyadic green s function for the spherical impedance boss at the edge is developed it is observed that the scattering is highly enhanced by the edge guided waves additionally using t matrix method the solution is extended to the general case of irregularly shaped scatterers the t matrix solution is verified by applying it to the case of a spherical scatterer and results are compared with the dyadic green s function solution

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

a small delay and correlation time limit of stochastic differential delay equations with state dependent colored noise we consider a general stochastic differential delay equation sdde with state dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero the work is motivated by an experiment involving an electrical circuit with noisy delayed feedback an ornstein uhlenbeck process is used to model the colored noise the main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by kurtz and protter and a maximal inequality for sums of a stationary sequence of random variables by peligrad and utev

fokker planck equations for time delayed systems via markovian embedding for stochastic systems with discrete time delay the fokker planck equation fpe of the one time probability density function pdf does not provide a complete self contained probabilistic description it explicitly involves the two time pdf and represents in fact only the first member of an infinite hierarchy we here introduce a new approach to obtain a fokker planck description by using a markovian embedding technique and a subsequent limiting procedure on this way we find a closed complete fpe in an infinite dimensional space from which one can derive a hierarchy of fpes while the first member is the well known fpe for the one time pdf we obtain as second member a new representation of the equation for the two time pdf from a conceptual point of view our approach is simpler than earlier derivations and it yields interesting insight into both the physical meaning and the mathematical structure of delayed processes we further propose an approximation for the two time pdf which is a central quantity in the description of these non markovian systems as it directly gives the correlation between the present and the delayed state application to a prototypical bistable system reveals that this approximation captures the non trivial effects induced by the delay remarkably well despite its surprisingly simple form moreover it outperforms earlier approaches for the one time pdf in the regime of large delays

efficient calculation of the electromagnetic dyadic green s function in spherical layered media a numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media the proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing helmholtz equation more specifically the finite difference solution of this equation may be cast in a pole residue form that allows the analytic evaluation of the spherical harmonics series by means of the watson transformation thus a closed form expression is obtained for the electromagnetic fields in terms of a short series of associated legendre functions p sup m sub spl nu cos spl theta of integer order m and complex degree spl nu the number of terms in the series is strongly dependent on the angle spl theta and decreases very fast when the point of observation moves away from the source the method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions

discrete models of electromagnetic wave scatterers in a frequency range we investigate the spatial and frequency characteristics of electromagnetic fields scattered by some object frequency functions that allow the expression of all elements of the object scatter matrix are introduced the sampling theorems that are proved for the introduced functions make it possible to characterize the scatterer by a set of discrete parameters the application of the proved theorems provides for the creation of a versatile scatterer discrete model that determines the dependence of scattered fields both on spatial coordinates and frequency a random scatterer is considered and the conditions under which the discrete parameters are statistically independent normalized random variables are stated the article presents the results of a random scatterer modeling

passage time statistics in exponential distributed time delay models noisy asymptotic dynamics the stochastic dynamics toward the final attractor in exponential distributed time delay non linear models is presented then the passage time statistic is studied analytically in the small noise approximation the problem is worked out by going to the associated two dimensional system the mean first passage time left langle t e right rangle from the unstable state for this non markovian type of system has been worked out using two different approaches firstly by a rigorous adiabatic markovian approximation in the small mean delay time epsilon lambda 1 secondly by introducing the stochastic path perturbation approach to get a non adiabatic theory for any lambda this first passage time distribution can be written in terms of the important parameters of the models we have compared both approaches and we have found excellent agreement between them in the adiabatic limit in addition using our non adiabatic approach we predict a crossover and a novel behavior for the relaxation scaling time as a function of the delay parameter which for lambda ll 1 goes as left langle t e right rangle sim 1 sqrt lambda

influence of strong noise on the decline and propagation of population in the delayed malthus verhulst model abstract the effects of strong noise on the decline and propagation processes of a population in the malthus verhulst model with time delay are investigated by a stochastic simulation time delays in two different processes are concurrent in ecosystems the simulation results indicate that the stability of the population is enhanced by the decreasing multiplicative noise intensity and the increasing delay time the replacement of old individuals with young ones is accelerated by an increasing multiplicative noise intensity an increasing additive noise intensity and a decreasing delay time an increasing multiplicative noise intensity will drive the population of species to fluctuate more largely

control of noise induced oscillations by delayed feedback abstract we propose a method to control noise induced motion based on using delayed feedback in the form of the difference between the delayed and the current states of the system the method is applied to two different types of systems namely a self oscillator near andronov hopf bifurcation and a threshold system in both cases we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations the entrainment of the basic period of oscillations by time delay is discovered we give explanations of the phenomena observed and provide a theory for the system near bifurcation

effects of time delay on symmetric two species competition subject to noise noise and time delay act simultaneously on real ecological systems the lotka volterra model of symmetric two species competition with noise and time delay was investigated in this paper by means of stochastic simulation we find that i the time delay induces the densities of the two species to periodically oscillate synchronously ii the stationary probability distribution function of the two species densities exhibits a transition from multiple to single stability as the delay time increases iii the characteristic correlation time for the sum of the two species densities squared exhibits a nonmonotonic behavior as a function of delay time our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems

on the eigenfunction expansion of electromagnetic dyadic green s functions a relatively simple approach is described for developing the complete eigenfunction expansion of time harmonic electric bar e and magnetic bar h fields within exterior or interior regions containing an arbitrarily oriented electric current point source in particular these results yield directly the complete eigenfunction expansion of the electric and magnetic dyadic green s functions bar bar g e and bar bar g m that are associated with bar e and bar h respectively this expansion of bar bar g e and bar bar g m contains only the solenoidal type eigenfunctions in addition the expansion of bar bar g e also contains an explicit dyadic delta function term which is required for making that expansion complete at the source point the explicit dyadic delta function term in bar bar g e is found readily from a simple condition governing the behavior of the eigenfunction expansion at the source point provided one views that condition in the light of distribution theory these general expressions for the eigenfunction expansion of bar bar g e and bar bar g m reduce properly to those obtained previously for special geometries by tai

a model based parameter estimation technique for wide band interpolation of periodic moment method impedance matrices with application to genetic algorithm optimization of frequency selective surfaces a model based parameter estimation mbpe technique is introduced in this paper for efficiently interpolating periodic moment method pmm impedance matrices over a wide frequency band in the model only the floquet harmonics that strongly affect the frequency band of interest are employed to approximate the matrix elements while the contributions from all other higher order harmonics are compactly represented by two additional terms the derivation of the model is physics based and the objective is to find the coefficients of the terms in the model by utilizing the values of the impedance matrix elements calculated via pmm at only a few frequency points the number and position of these fitting points can be pre determined from the cutoff frequencies of the floquet harmonics which allows the mbpe interpolation process in this case to be completely automated in other words the number and position of the sampling points are only dictated by the periodicity of the frequency selective surface fss structure and the frequency range of interest unlike many of the other scattering parameter based techniques the shape and the resonances in the response of the fss do not have any impact on the construction of the interpolation model this makes it particularly useful in genetic algorithm ga aided fss design since for a fixed periodicity and frequency range the mbpe interpolation is independent of the scattering response of candidate fss designs several examples of the new pmm mbpe approach are presented including one in which it is used to considerably speed up the ga based design process for a reconfigurable fss

analytical results for fundamental time delayed feedback systems subjected to multiplicative noise we study the stochastic behavior of fundamental time delayed feedback systems subjected to multiplicative noise we derive exact results for the first and second moments and the autocorrelation function for a particular class of systems we show how the variance depends on the amplitude of the multiplicative noise furthermore we identify parameter regions of stationary solutions with finite and infinite variances finally we suggest that delay induced levy flights may occur in time delayed feedback systems involving multiplicative noise

a new stochastic gompertz diffusion process with threshold parameter computational aspects and applications abstract in this paper we propose a new homogeneous stochastic gompertz diffusion model with a threshold parameter this can be considered an extension of the homogeneous three parameter gompertz process with the addition of a fourth parameter from the corresponding kolmogorov equations and ito s stochastic differential equations we obtain the transition probability density function and the moments of this process specifically the trend functions the parameters are estimated by considering discrete sampling of the sample path of the model and by using maximum likelihood methodology estimation of the threshold parameter requires us to solve a non linear equation which is achieved by the newton raphson method simulated model data are considered and the methodology in question is applied to estimate the parameters the values obtained are compared with those used in the simulation finally the model is applied to model the evolution of the trend of the dynamic variable average monthly salary cost for all sectors and broken down construction industry services in spain for the period 1985 2005

exact statistics for linear time delayed oscillators subjected to gaussian excitation abstract large classes of stochastic systems of interest to acoustics and vibrations have time delays the presence of these time delays hinders efforts to provide physical insight into the system behavior because of the difficulty of finding exact solutions this paper addresses this issue by presenting exact steady state solutions for the probability density functions pdf s for linear time delayed oscillators subjected to gaussian excitation of arbitrary correlation a key parameter influencing these pdf s is shown to be the ratio of mean generalized kinetic energy to the mean generalized potential energy in a single damped harmonic oscillator this ratio is unity which implies an equi partition of generalized energy time delays cause deviations in the equi partition of generalized energy which creates regions of preferential total phase and causes the amplitude pdf to shift from a rayleigh distribution to a hoyt distribution

stochastic resonance in time delayed bistable systems driven by weak periodic signal abstract we study theoretically a bistable system with time delayed feedback driven by a weak periodic force the effective potential function and the steady state probability density are derived the delay time and the strength of its feedback can change the shapes of the potential wells in the adiabatic approximation the signal to noise ratio snr of the system with a weak periodic force is obtained the time delayed feedback modulates the magnitude of snr by changing the shape of the potential and the effective strength of the signal the maximum of snr decreases with increasing the feedback intensity when is negative or positive the time delay can suppress or promote the stochastic resonance phenomenon

frequency adaptation in controlled stochastic resonance utilizing delayed feedback method two pole approximation for response function stochastic resonance sr enhanced by time delayed feedback control is studied the system in the absence of control is described by a langevin equation for a bistable system and possesses a usual sr response the control with the feedback loop the delay time of which equals to one half of the period 2 of the input signal gives rise to a noise induced oscillatory switching cycle between two states in the output time series while its average frequency is just smaller than in a small noise regime as the noise intensity d approaches an appropriate level the noise constructively works to adapt the frequency of the switching cycle to and this changes the dynamics into a state wherein the phase of the output signal is entrained to that of the input signal from its phase slipped state the behavior is characterized by power loss of the external signal or response function this paper deals with the response function based on a dichotomic model a method of delay coordinate series expansion which reduces a non markovian transition probability flux to a series of memory fluxes on a discrete delay coordinate system is proposed its primitive implementation suggests that the method can be a potential tool for a systematic analysis of sr phenomenon with delayed feedback loop we show that a d dependent behavior of poles of a finite laplace transform of the response function qualitatively characterizes the structure of the power loss and we also show analytical results for the correlation function and the power spectral density

the model based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy to this end interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced order pade spl acute rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth the use of this piece wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies in this paper exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation the technique is applied to the case of a 0 5 meter dipole modeled from 150 to 950 mhz and for spl theta from 0 spl deg to 90 spl deg using fitting windows with three and four sampling frequencies the results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure in the spatial domain spherical harmonics are introduced as model based fitting functions for antenna radiation patterns specifically interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one and two dimensional far field radiation patterns respectively the case of a z oriented 0 5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically based fitting models in the spatial domain zonal harmonics are used to interpolate far field radiation patterns of this antenna for spl theta from 0 spl deg to 180 spl deg for several different frequencies over the range from 150 to 950 mhz this example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain

fokker planck description for a linear delayed langevin equation with additive gaussian noise we construct an equivalent probability description of linear multi delay langevin equations subject to additive gaussian white noise by exploiting the time convolutionless transform and a time variable transformation we are able to write a fokker planck equation fpe for the 1 time and for the 2 time probability distributions valid irrespective of the regime of stability of the langevin equations we solve exactly the derived fpes and analyze the aging dynamics by studying analytically the conditional probability distribution we discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non markov process as both preparation and observation times have bearing on its dynamics as our analytic procedure can also be applied to linear langevin equations with memory kernels we compare the non markov dynamics of a one delay system with that of a generalized langevin equation with an exponential as well as a power law memory application to a generalization of the green kubo formula is also presented

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

stochastic order parameter equation of isometric force production revealed by drift diffusion estimates we address two questions that are central to understanding human motor control variability what kind of dynamical components contribute to motor control variability i e deterministic and or random ones and how are those components structured to this end we derive a stochastic order parameter equation for isometric force production from experimental data using drift diffusion estimates we show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity a structural analysis reveals that the deterministic component consists of a linear control loop while the random component involves a noise source that scales with force output in addition we present evidence for the existence of a subject independent overall noise level of human isometric force production

non gaussian noise weakened stability in a foraging colony system with time delay abstract in this paper the dynamical properties in a foraging colony system with time delay and non gaussian noise were investigated using delay fokker planck approach the stationary probability distribution spd the associated relaxation time art and normalization correlation function ncf are obtained respectively the results show that i the time delay and non gaussian noise can induce transition from a single peak to double peaks in the spd i e a type of bistability occurring in a foraging colony system where time delay and non gaussian noise not only cause transitions between stable states but also construct the states themselves numerical simulations are presented and are in good agreement with the approximate theoretical results ii there exists a maximum in the art as a function of the noise intensity this maximum for art is identified as the characteristic of the non gaussian noise weakened stability of the foraging colonies in the steady state iii the art as a function of the noise correlation time exhibits a maximum and a minimum where the minimum for art is identified as the signature of the non gaussian noise enhanced stability of the foraging colonies and iv the time delay can enhance the stability of the foraging colonies in the steady state while the departure from gaussian noise can weaken it namely the time delay and departure from gaussian noise play opposite roles in art or ncf

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

the simultaneous interpolation of antenna radiation patterns in both the spatial and frequency domains using model based parameter estimation the pade rational function fitting model commonly used for model based parameter estimation mbpe in the frequency domain is enhanced to include spatial dependence in the numerator and denominator coefficients this allows the function to interpolate an antenna radiated electric field pattern in both the frequency and spatial domains simultaneously such that a single set of coefficients can be used to accurately reconstruct an entire radiation pattern at any frequency in the fitting model range a simple procedure is introduced for transforming interpolated electric fields into gain patterns using input impedance versus frequency curves also obtained via mbpe the utility of this method is demonstrated by applying it to a dipole antenna over a frequency range of 150 950 mhz and using a polynomial representation in spl theta for the coefficient spatial dependence it is also used to estimate radiation patterns for a three element yagi array between the frequencies of 470 and 500 mhz using a binomial representation for the spatial variation that includes terms dependent on spl theta as well as spl phi the use of this method for interpolating radiation patterns has at least two significant advantages one being large compression ratios for the amount of data that must be stored to accurately reproduce patterns and the other being a significant decrease in the amount of time required for modeling problems with large computational domains

bifurcations in fluctuating systems the center manifold approach bifurcations in fluctuating dynamical systems are studied using the ideas of center manifold reduction the method provides not only a systematic procedure for the reduction of the system to a small number of variables but also a classification scheme for the different kinds of dynamical behavior possible near bifurcation points the joint probability density factorizes into a stationary gaussian densityp v u in the fast variablesv and a time dependent densityp u f in the slow variablesu describing the dynamics on the center manifoldv v0 u p u t obeys a reduced fokker planck equation that can be written in a normal form by means of local nonlinear transformations both additive and multiplicative white noise are considered as is colored noise the results extend and formalize haken s concept of adiabatic elimination of fast variables

augmented moment method for stochastic ensembles with delayed couplings ii fitzhugh nagumo model dynamics of fitzhugh nagumo fn neuron ensembles with time delayed couplings subject to white noises has been studied by using both direct simulations and a semianalytical augmented moment method amm which has been proposed in a preceding paper h hasegawa phys rev e 70 021911 2004 for n unit fn neuron ensembles amm transforms original 2n dimensional stochastic delay differential equations sddes to infinite dimensional deterministic des for means and correlation functions of local and global variables infinite order recursive des are terminated at the finite level m in the level m amm mathrm amm m yielding 8 m 1 dimensional deterministic des when a single spike is applied the oscillation may be induced if parameters of coupling strength delay noise intensity and or ensemble size are appropriate effects of these parameters on the emergence of the oscillation and on the synchronization in fn neuron ensembles have been studied the synchronization shows the fluctuation induced enhancement at the transition between nonoscillating and oscillating states results calculated by amm5 are in fairly good agreement with those obtained by direct simulations

orbit closures in the enhanced nilpotent cone we study the orbits of g gl v in the enhanced nilpotent cone where is the variety of nilpotent endomorphisms of v these orbits are parametrized by bipartitions of n dimv and we prove that the closure ordering corresponds to a natural partial order on bipartitions moreover we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of kostka polynomials defined by shoji finally we make a connection with kato s exotic nilpotent cone in type c proving that the closure ordering is the same and conjecturing that the intersection cohomology is the same but with degrees doubled

augmented moment method for stochastic ensembles with delayed couplings i langevin model by employing a semianalytical dynamical mean field approximation theory previously proposed by the author h hasegawa phys rev e 67 041903 2003 we have developed an augmented moment method amm in order to discuss dynamics of an n unit ensemble described by langevin equations with delays in an amm original n dimensional stochastic delay differential equations sddes are transformed to infinite dimensional deterministic des for means and correlations of local as well as global variables infinite order des arising from the non markovian property of sdde are terminated at the finite level m in the level m amm mathrm amm m which yields 3 m dimensional deterministic des model calculations have been made for linear and nonlinear langevin models the stationary solution of amm for the linear langevin model with n 1 is nicely compared to the exact result in the nonlinear langevin ensemble the synchronization is shown to be enhanced near the transition point between the oscillating and nonoscillating states results calculated by amm6 are in good agreement with those obtained by direct simulations

influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise the influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied applying small delay time approximation under the adiabatic limit condition the expression of the signal to noise ratio snr of the system is obtained it is found that the snr varies non monotonously with the delayed time and the correlation of the colored noise moreover the snr exhibits sr behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise and as a function of the strength of the colored noise

multivariate markov processes for stochastic systems with delays application to the stochastic gompertz model with delay using the method of steps we describe stochastic processes with delays in terms of markov diffusion processes thus multivariate langevin equations and fokker planck equations are derived for stochastic delay differential equations natural periodic and reflective boundary conditions are discussed both ito and stratonovich calculus are used in particular our fokker planck approach recovers the generalized delay fokker planck equation proposed by guillouzic et al the results obtained are applied to a model for population growth the gompertz model with delay and multiplicative white noise

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

on reducible nonlinear time delayed stochastic systems fluctuation dissipation relations transitions to bistability and secondary transitions to non stationarity we show the conditions under which nonlinear time delayed dynamical systems with multiplicative noise sources can be transformed into linear time delayed systems with additive noise sources we show that for such reducible systems analytical expressions for stationary distributions can be obtained we demonstrate that fluctuation dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay and noise induced transitions to bistability and secondary transitions to non stationarity our general findings are exemplified for three models a gompertz model a hongler model and a model involving a 1 x 2 noise amplitude

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

pitchfork and hopf bifurcation thresholds in stochastic equations with delayed feedback the bifurcation diagram of a model stochastic differential equation with delayed feedback is presented we are motivated by recent research on stochastic effects in models of transcriptional gene regulation we start from the normal form for a pitchfork bifurcation and add multiplicative or parametric noise and linear delayed feedback the latter is sufficient to originate a hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback we find a sharp bifurcation in parameter space and define the threshold as the point in which the stationary distribution function p x changes from a delta function at the trivial state x 0 to p x approximately x alpha at small x with alpha 1 exactly at threshold we find that the bifurcation threshold is shifted by fluctuations relative to the deterministic limit by an amount that scales linearly with the noise intensity analytic calculations of the bifurcation threshold are also presented in the limit of small delay tau 0 that compare quite favorably with the numerical solutions even for moderate values of tau

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

fokker planck perspective on stochastic delay systems exact solutions and data analysis of biological systems stochastic delay systems with additive noise are examined from the perspective of fokker planck equations for a linear system the exact stationary probability density is derived by means of a delay fokker planck equation we show how to determine the delay equation of the linear system from experimental data and corroborate a fundamental result previously obtained by kuchler and mensch we also propose a method to derive delay equations of nonlinear systems from experimental data to this end the theory of multivariate fokker planck equations is used the applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans

stochastic differential delay equation moment stability and application to hematopoietic stem cell regulation system we study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise the results established here are applied to examining the local stability of the hematopoietic stem cell hsc regulation system in the presence of noise the stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system however the stability of the second moment is altered by the perturbation we obtain using laplace transform techniques necessary and sufficient conditions for the second moment to be bounded in applying the results to the hsc system we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates but insensitive to perturbations in the proliferation rate

noise induced global asymptotic stability we prove analytically that additive and parametric multiplicative gaussian distributed white noise interpreted in either the it6 or stratonovich formalism induces global asymptotic stability in two prototypical dynamical systems designated as supercritical the landau equation and subcritical respectively in both systems without noise variation of a parameter leads to a switching between a single globally stable steady state and multiple locally stable steady states with additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter however parametric noise causes a noise amplitude dependent shift postponement in the parameter value at which the switching occurs it is shown analytically that the density converges to a dirac delta function when the solution of the fokker planck equation is no longer normalizable

oscillatory correlation of delayed random walks we investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence delayed random walk the characteristic feature of such a model is the oscillatory behavior of its correlation function we investigate a model whose transient and stationary oscillatory behavior is analytically tractable the correspondence of the model with a langevin equation with delay is also considered

stochastic resonance in a tumor immune system subject to bounded noises and time delay abstract immunotherapy is one of the most recent approaches in cancer therapy a mathematical model of tumor immune interaction subject to a periodic immunotherapy treatment imitated by a periodic signal correlative and bounded stochastic fluctuations and time delays is investigated by numerical simulations for its signal power amplification spa within the tailored parameter regime the synchronous response of tumor growth to the immunotherapy stochastic resonance sr versus both the noises and delays is obtained the details are as follows i the peak values of spa versus the noise intensity a in the proliferation term of tumor cells decrease as the frequency of periodic signal increases i e an increase of the frequency restrains the sr ii an increase of the amplitude of periodic signal restrains the sr versus a but boosts up the sr versus the noise intensity b in the immune term iii there is an optimum cross correlated degree between the two bounded noises at which the system exhibits the strongest sr versus the delay time the reaction time of tumor cell population to their surrounding environment constraints iv upon increasing the delay time double sr versus the delay time the time taken by both the tumor antigen identification and tumor stimulated proliferation of effectors emerges these results may be helpful for an immunotherapy treatment for the sufferer

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

a novel technique for the approximation of 3 d antenna radiation patterns in this paper a novel technique for the approximation of three dimensional 3 d antenna radiation patterns is presented the proposed method combines the two principal cuts in order to acquire an adequate estimate of the 3 d antenna radiation solid the absolute error from the theoretical solution is analyzed along with other statistical measures for various types of antenna structures namely omni directional and directive arrays the performance of the method is compared against other existing extrapolation algorithms the proposed technique exhibits low approximation errors and is easily integrated into 3 d radio propagation planning tools such as ray tracing algorithms

coherence of noisy oscillators with delayed feedback a theory ofe ect ofdelayed f on the coherence ofthe noisy self sustained oscillations is developed in the gaussian approximation a closed system ofequations is derived f the phase di usion constant and the mean frequency a comparison with numerics shows that the theory works well for weak feedback and strong noise c

the resonance mode theory for exterior problems of electrodynamics and its application to discrete antenna modeling in a frequency range the problem under consideration here is that of building a versatile discrete antenna model in a frequency range the eigenfunction mode expansion or singularity expansion method sem is used in working out the problem a detailed substantiation of sem is provided and an expression determining the dependence of mode amplitudes on exterior source fields is derived a simple example is provided in support of the theory the sem is used in inquiring into the frequency dependence of antenna generalized matrix entries it is intimated that all of the matrix entries contain resonance factors and factors that are hankel transforms of radial coordinate functions a sampling theorem which is a generalized extension of the classic sampling theorem is used for the hankel transform the application of the generalized sampling theorem completes the process of building a versatile discrete antenna model in a frequency range

delayed stochastic systems noise and time delay are two elements that are associated with many natural systems and often they are sources of complex behaviors understanding of this complexity is yet to be explored particularly when both elements are present as a step to gain insight into such complexity for a system with both noise and delay we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives a langevin equation with delay and a random walk model whose transition probability depends on a fixed time interval past delayed random walk model are the subjects of in depth focus as well as considering relations between these two types of models we derive an approximate fokker planck equation for delayed stochastic systems and compare its solution with numerical results

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

delay fokker planck equations novikov s theorem and boltzmann distributions as small delay approximations we study time delayed stochastic systems that can be described by means of so called delay fokker planck equations using novikov s theorem we first show that the theory of delay fokker planck equations is on an equal footing with the theory of ordinary fokker planck equations subsequently we derive stationary distributions in the case of small time delays in the case of additive noise systems these distributions can be cast into the form of boltzmann distributions involving effective potential functions

stochastic resonance in a bistable system subject to multi time delayed feedback and aperiodic signal we discuss in detail the effects of the multi time delayed feedback driven by an aperiodic signal on the output of a stochastic resonance sr system the effective potential function and dynamical probability density function pdf are derived to measure the performance of the sr system in the presence of a binary random signal the bit error rate ber defined by the dynamical pdf is employed as is commonly used in digital communications we find that the delay time strength of the feedback and number of time delayed terms can change the effective potential function and the effective amplitude of the signal and then affect the ber of the sr system the numerical simulations strongly support the theoretical results the goal of this investigation is to explore the effects of the multi time delayed feedback on sr and give a guidance to nonlinear systems in the application of information processing

stationary distributions of stochastic processes described by a linear neutral delay differential equation stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation the distributions are gaussian distributions the variances of the gaussian distributions are either monotonically increasing or decreasing functions of the time delays the variances become infinite when fixed points of corresponding deterministic processes become unstable

the exotic nilcone of a symplectic group abstract let g be the symplectic group s p 2 n k k an algebraically closed field of characteristic 2 it acts in v k 2 n the exotic nilcone of g is the nilcone in the sense of invariant theory of the g module v 2 v the paper discusses elementary properties of the g action on the exotic nilcone

a spherical wave representation of the dyadic green s function for a wedge a new expansion for the dyadic green s function of a perfectly conducting wedge is derived it is expressed in terms of a discrete series of spherical vector wave functions this expansion converges well except near a spherical surface which passes through the source point the convergence is particularly rapid in the paraxial region this results in the identification of an edge wave which can play an important role in the radiation from sources and scatterers at the edge of the wedge

stationary solutions of linear stochastic delay differential equations applications to biological systems recently k uchler and mensch stochastics stochastics rep 40 23 1992 derived exact stationary probability densities for linear stochastic delay differential equations this paper presents an alternative derivation of these solutions by means of the fokker planck approach introduced by guillouzic phys rev e 59 3970 1999 61 4906 2000 applications of this approach which is argued to have greater generality are discussed in the context of stochastic models for population growth and tracking movements

parametric modeling of radiation patterns and scattering parameters of antennas this paper describes a data driven method to model the radiation patterns over a large angular region and scattering parameters of antennas as a function of the geometry of the antenna the radiation pattern model consists of a linear combination of characteristic basis function patterns cbfps where the expansion coefficients of the cbfps are the functions of geometrical features of the antenna scattering parameters are modeled by means of parameterized state space matrices the obtained models are quick to evaluate and are thus suitable for design activities where multiple simulations are required the proposed method is validated through illustrative examples

adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations this paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays mixed delays as well as uncertain nonlinear external and stochastic perturbations hybrid perturbations a simple but robust adaptive controller is designed such that the response system can lag synchronize with a drive system based on the lyapunov stability theory and some suitable lyapunov krasovskii functionals several sufficient conditions ensuring the lag synchronization are developed our synchronization criteria are easily verified and do not need to solve any linear matrix inequality some existing results are improved and extended moreover the designed adaptive controller has better anti interference capacity and is more practical than the usual adaptive controller numerical simulations are exploited to show the effectiveness of the theoretical results

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

equivalent layers of surface charge current sheet and polarization in the eigenfunction expansions of green s functions in electromagnetic theory the discontinuous behavior of the eigenfunction expansion of various green s functions commonly used in electromagnetic theory is discussed with the aid of equivalent layers of surface charge current sheet and surface polarization green s function pertaining to the potential function in electrostatics is discussed first followed by a detailed analysis of an eigenfunction representation of a typical dyadic green s function for time varying harmonic fields