transient properties of a bistable kinetic model with correlations between additive and multiplicative noises mean first passage time the transient properties of a bistable system with correlations between additive and multiplicative noise terms are investigated the explicit expressions of the mean first passage time mfpt are obtained the numerical computations show that the mfpt of the system is affected by ensuremath lambda the strength of correlations between additive intensity ensuremath alpha and multiplicative intensity d noise terms for the case of perfectly correlated noises ensuremath lambda 1 the mfpt corresponding to ensuremath alpha ensuremath gtrsim d and ensuremath alpha d exhibits very different behaviors and the mfpt for ensuremath alpha d diverges to infinity textcopyright 1996 the american physical society

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

stochastic system with colored correlation between white noise and colored noise abstract a stochastic system with colored correlation between white noise and colored noise is investigated theoretically a general fokker planck equation of the system is derived by using a standard method we discuss a bistable system with colored correlation between additive white noise and multiplicative colored one it is found that the effects of the correlation time of multiplicative colored noise on the statistical properties of the bistable system are different from those of the correlation time of the correlation between additive white noise and multiplicative colored noise on the statistical properties of the bistable system

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

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

effects of nonlocal feedback on traveling fronts in neural fields subject to transmission delay the work introduces a model for reciprocal connections in neural fields by a nonlocal feedback mechanism while the neural field exhibits nonlocal interactions and intra areal transmission delays we study the speed of traveling fronts with respect to the transmission delay the spatial feedback range and the feedback delay for general axonal and feedback connectivity kernels in addition we find a novel shape of traveling fronts due to the applied feedback and criteria for its occurence are derived

a branch and bound approach to the bicriterion scheduling problem invloving total flowtime and range of lateness this paper considers a bicriterion scheduling problem where a linear combination of two objective functions is considered with weighting factors used to represent relative importance of the two criteria i e total flowtime and range of lateness a branch and bound solution procedure is designed for the problem computational results are also reported

effect of non gaussian noise sources in a noise induced transition here we study a noise induced transition when the system is driven by a noise source taken as colored and non gaussian we show using both a theoretical approximation and numerical simulations that there is a shift of the transition as the noise departs from the gaussian behavior also we confirm the reentrance effect found for colored gaussian noise and show the behavior of the transition line in the phase like diagram as the noise departs from gaussianity in the large correlation time limit

computing the degree of determinants via combinatorial relaxation let a x a ij x be a square matrix with a ij being a polynomial in x this paper proposes combinatorial relaxation type algorithms for computing the degree of the determinant delta a deg x det a x based on its combinatorial upper bound widehat delta a which is defined in terms of the maximum weight of a perfect matching in an associated graph the graph is bipartite for a general square matrix a and nonbipartite for a skew symmetric a the algorithm transforms a to another matrix a for which delta a delta a widehat delta a with successive elementary operations the algorithm is efficient making full use of the fast algorithms for weighted matchings it is combinatorial in almost all cases or generically and invokes algebraic elimination routines only when accidental numerical cancellations occur it is shown in passing that for a skew symmetric polynomial matrix a x there exists a unimodular matrix u x such that a x u x a x u x tp satisfies delta a delta a widehat delta a

colored multiplicative and additive non gaussian noise driven dynamical system mean first passage time abstract we have studied the barrier crossing dynamics in presence of non gaussian noises it has been observed that multiplicative colored non gaussian noise can induce resonant activation ra the conspicuous dependence of mean first passage time mfpt on correlation time 2 of additive colored noise having fixed variance have been analyzed beyond a critical value of 2 the mfpt increases for a given rate of increase of noise strength with 2 if the additive colored noise is non gaussian the mfpt first decreases with increase of the non gaussian parameter measures deviation from gaussian character of multiplicative colored noise followed by an increase exhibiting a minimum the appearance of the minimum critically depends on the additive noise

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

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

the generic canonical form of a regular structured matrix pencil abstract we consider a matrix pencil consisting of two square structured matrices of the same dimensions where we call a matrix structured if we only know its zero nonzero pattern replacing each nonzero by a parameter we obtain a parametrization of the matrix pencil in this paper we assume that for almost all possible parameter values the matrix pencil is regular i e has a nonzero determinant given such a regular structured matrix pencil we present graph theoretic methods to obtain its so called generic canonical form described by the zero structures at s 0 zero structure at the point zero and s zero structure at the point infinity and the number of finite zeros outside s 0 zeros outside s 0 and s which will be shown to be mutually distinct here the word generic indicates that the obtained canonical form will be of the same shape for almost all possible parameter values the presented methods are related to well known and efficient methods from combinatorial optimization

trichotomous noise induced transitions a nonlinear one dimensional process driven by a multiplicative exponentially correlated three level markovian noise trichotomous noise is considered an explicit second order linear ordinary differential equation for the stationary probability density distribution is obtained for the process in the case of a linear process with an additive trichotomous noise the exact formula for the steady state distribution is obtained the well known dichotomous noise can be regarded as a special case of the trichotomous noise as a rule the system variable has three specific values where the probability density distribution can be singular for the case of the hongler model the dependence of the behavior of the stationary probability density on the noise parameters is investigated in detail and illustrated by a phase diagram applications to the gompertz and verhulst models are also discussed

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

approximate fokker planck equation of system driven by multiplicative colored noises with colored cross correlation abstract using the hanggi ansatz to truncate the evolution equation for probability density an approximate fokker planck equation afpe is derived this afpe is valid for one dimensional general systems driven by two multiplicative colored noises 1 0 and 2 0 that are correlated in color 3 0 under the condition for 1 2 and 3 to satisfy some inequalities we apply this afpe to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross correlation to verify the validity of our analytical approximation the numerical simulations for this system is performed we discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self correlation time is increased

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

bistable kinetic model driven by correlated noises steady state analysis a simple rule to obtain the fokker planck equation for a general one dimensional system driven by correlated gaussian white noises is proved by the functional method the fokker planck equation obtained in this paper is applied to the bistable kinetic model we find the following for the steady state 1 in the ensuremath alpha d parameter plane ensuremath alpha is the strength of the additive noise and d is the multiplicative noise strength the critical curve separating the unimodal and bimodal regions of the stationary probability distribution spd of the model is shown to be affected by ensuremath lambda the degree of correlation of the noises as ensuremath lambda is increased the area of the bimodal region in the ensuremath alpha d plane is contracted 2 when we take a point fixed in the ensuremath alpha d plane and increase ensuremath lambda the form of the spd changes from a bimodal to a unimodal structure 3 the positions of the extreme value of the spd of the model sensitively depend on the strength of the multiplicative noise and weakly depend on the additive noise strength 4 for ensuremath lambda 1 the case of perfectly correlated noises when the parameters ensuremath alpha and d take values in the neighborhood of the line ensuremath alpha d in the ensuremath alpha d plane the spd s corresponding to the points ensuremath alpha dg1 and ensuremath alpha d1 exhibit a very different shape of divergence therefore the ratio ensuremath alpha d 1 plays the role of a critical ratio

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

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

subcritical hopf bifurcation in dynamical systems described by a scalar nonlinear delay differential equation a subcritical hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally the subcritical hopf bifurcation leads to a significant domain of bistability where stable steady and time periodic states coexist

numerical modelling in biosciences using delay differential equations our principal purposes here are i to consider from the perspective of applied mathematics models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics ii to review the application of numerical techniques to investigate these models we show that there are prima facie reasons for using such models i they have a richer mathematical framework compared with ordinary differential equations for the analysis of biosystem dynamics ii they display better consistency with the nature of certain biological processes and predictive results we analyze both the qualitative and quantitative role that delays play in basic time lag models proposed in population dynamics epidemiology physiology immunology neural networks and cell kinetics we then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences comparing them with those implemented by the bio modellers

a stochastic model of indopacific sea surface temperature anomalies abstract it is often desirable to represent a rapidly varying physical process as stochastic forcing of some slower dynamical system a review of this approximation is presented the white noise limit of rapidly varying processes reduces the dynamical description of the affected slower systems to stochastic differential equations the properties of which are summarized as an application of stochastic differential equations we review the evidence that indopacific sea surface temperature anomalies sstas can be represented as a stable linear process driven by spatially coherent stochastic forcing an inversemodeling approach is used that is the relevant parameters of the best fit stable linear process are obtained from observations and given these parameters the assumptions of stability and linearity are subsequently tested an optimal initial structure for growth predicted by the model is found to occur approximately seven months before most of the major warm and cold el nino la nina events in the data record the optimal structure preferentially occurs in the boreal spring with the mature phase of the extreme event occurring in the subsequent late fall winter the best model to fit the observations including the dependence of the dynamical system on the annual cycle is driven by stochastic forcing with periodic statistics these statistics are inferred using a time dependent fluctuation dissipation relation the variation of the stochastic forcing with the annual cycle is not the same as that of the optimal initial structure yet when a linear numerical model is driven with the derived stochastic forcing the optimal structure including its variation with the annual cycle is recovered this implies that deterministic dynamics play an important role in setting up the optimal structure and therefore a mature phase of el nino may be predicted before the optimal structure actually appears

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

response probability density functions of duffing van der pol vibro impact system under correlated gaussian white noise excitations abstract this paper aims to investigate the stationary probability density functions pdfs of a duffing van der pol vibro impact system excited by correlated gaussian white noise with the help of non smooth transformation the stationary pdfs are formulated analytically by the stochastic averaging of energy envelope the analytical results are verified by numerical simulation results stochastic bifurcations for different parameters are considered and several special pdf forms are observed in this paper the first form is the shape of the pdf of total energy can be similar to a crater which has a minimum and a maximum the second one is the shape of the joint pdf with three peaks that is to say the section of joint pdf has three maximum and two minimum in addition the influence of the degree of the correlation of gaussian white noises is explored

a moment approach to non gaussian colored noise abstract the langevin system subjected to non gaussian colored noise has been discussed by using the second order moment approach with two kinds of models for generating the noise we have derived the effective differential equation de for a variable x from which the stationary probability distribution p x has been calculated with the use of the fokker planck equation the result of p x calculated by the moment method is compared to several expressions obtained by different methods such as the universal colored noise approximation ucna jung and hanggi phys rev a 35 1987 4464 and the functional integral method it has been shown that our p x is in good agreement with that of direct simulations dss we have also discussed dynamical properties of the model with an external input solving des in the moment method

stochastic resonance nonperturbative calculation of power spectra and residence time distributions we examine the response of a finite temperature two state system to periodic driving using time dependent transition rate theory this system can exhibit the phenomenon of stochastic resonance where raising the temperature increases the signal to noise ratio of the response we obtain the power spectrum and the distribution of residence times nonperturbatively for any transition rates that are periodic in time given the drive period mathit t mathit s the power spectrum is the fourier transform of the sum of signal which is periodic in time with period mathit t mathit s and noise which is the product of an exponential and a function periodic with period mathit t mathit s the residence time distribution is the product of an exponential and a function that is periodic with period mathit t mathit s both the power spectrum and the residence time distribution can be calculated exactly given the dependence of the transition rates on the control parameter e g asymmetry or temperature we calculate the characteristics of stochastic resonance for a two state system with activated transition rates and for a quantum mechanical dissipative two level system

functional characterization of generalized langevin equations we present an exact functional formalism to deal with linear langevin equations with arbitrary memory kernels and driven by an arbitrary noise structure characterized through its characteristic functional no other hypothesis is assumed over the noise neither do we use the fluctuation dissipation theorem we find that the characteristic functional of the linear process can be expressed in terms of noise functional and the green function of the deterministic memory like dissipative dynamics this yields a procedure for calculating the full kolmogorov hierarchy of the non markov process as examples we have characterized through the 1 time probability a noise induced interplay between the dissipative dynamics and the structure of different noises conditions that lead to non gaussian statistics and distributions with long tails are analysed the introduction of arbitrary fluctuations in fractional langevin equations has also been pointed out

analytical evaluation of multi criteria heuristics this paper considers the problem of evaluating the solution quality of multi criteria heuristics by assuming an additive multi attribute value structure efficient and heuristic solutions can be translated into value measures that depend only on the relative importance assigned to the criteria of interest approximation errors are then defined as the value penalty incurred by approximating an efficient solution with its heuristic alternative results are derived which can be used to eliminate solutions that cannot represent the best available alternative among the set of efficient and heuristic solutions for the bicriterion case a polynomial algorithm for determining the mean and maximum relative heuristic error for a given problem instance is presented for more general multi criteria problems the maximum relative approximation error can be determined by solving a series of linear programming problems

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

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

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

stochastic resonance in discrete kinetics with delay abstract multiplicative stochastic resonance in linear systems with delay is studied for the discrete case the overdamped linear system with symmetric multiplicative markovian dichotomous noise dn is considered the stability range of the solutions for different values of delay is analyzed the maximum of the signal to noise ratio is observed as a function of the noise intensity

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

effect of time delay in fitzhugh nagumo neural model with correlations between multiplicative and additive noises abstract we study the effect of time delay in the fitzhugh nagumo neural model with correlations between multiplicative and additive noise terms based on the corresponding fokker planck equation the explicit expressions of the stationary probability distribution function spdf the mean first passage time mfpt and the signal to noise ratio snr are obtained respectively research results show that i the system undergoes a succession of two phase transitions i e the reentrance phenomenon as the noise correlation parameter is increased and a single phase transition as the time delay is increased ii the mfpt as a function of the multiplicative noise intensity exhibits a maximum this maximum for mfpt identifies the noise enhanced stability nes effect the noise correlation parameter intensifies the nes effect while the time delay and the additive noise intensity weakens it iii the existence of a maximum in the snr as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance sr phenomenon the noise correlation parameter enhances the sr while the time delay and the additive noise intensity weaken it

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

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

stochastic system with coupling between non gaussian and gaussian noise terms a stochastic system with coupling between non gaussian and gaussian noise terms is investigated a general approximate fokker planck equation of the system is derived through a path integral approach for a bistable system the coupling between noise terms can induce the reentrance like phase transition while the parameter q of the departure from the gaussian noise can induce the first order like phase transition both the coupling and the parameter q can change the curve of the mean first passage time mfpt from monotonically decreasing function to a peak in the mfpt numerical simulations are carried out to check the approximate theoretical results reasonably good agreement is obtained

asymmetric probability densities in symmetrically modulated bistable devices a brownian particle hopping in a symmetric double well potential can be statistically confined into a single well by the simultaneous action of a two periodic input signals one tilting the minima and the other one modulating the barrier height and b an additive and a purely multiplicative random signal generated by a unique source and thus preserving a certain degree of statistical correlation the underlying gating mechanism is quite robust when compared for instance with biharmonic rocking in view of technological implementation asymmetric confinement through gating can be conveniently maximized by tuning the input signal parameters correlation time phase time lag amplitudes thus revealing a resonant localization mechanism of general applicability

the study on a stochastic system with non gaussian noise and gaussian colored noise abstract in this paper a stochastic system with correlation between non gaussian noise and gaussian colored noise is investigated we carry out the functional methods to derive the approximate fokker planck equation and the expressions of stationary probability density function and mean first passage time are presented also we explore the effects of correlation between non gaussian and gaussian noise for the mean first passage time

analytic efficient solution set for multi criteria quadratic programs abstract we present active set methods to evaluate the exact analytic efficient solution set for multi criteria convex quadratic programming problems mcqp subject to linear constraints the idea is based on the observations that a strictly convex programming problem admits a unique solution and that the efficient solution set for a multi criteria strictly convex quadratic programming problem with linear equality constraints can be parameterized the case of bi criteria quadratic programming bcqp is first discussed since many of the underlying ideas can be explained much more clearly in the case of two objectives in particular we note that the efficient solution set of a bcqp problem is a curve on the surface of a polytope the extension to problems with more than two objectives is straightforward albeit some slightly more complicated notation two numerical examples are given to illustrate the proposed methods

effects of small time delay on a bistable system subject to levy stable noise l vy stable noise is often used to describe impulsive noise bursting in communication systems this paper investigates the effects of small time delay on a bistable system driven by an aperiodic bipolar pulse signal and l vy stable noise we obtain the dynamical probability density of the system response by solving the approximated time delayed fractional fokker planck equation ffpe via an implicit finite difference method a new approach to evaluate the system response time is presented the bit error rate ber is employed to measure the performance of the bistable system in detecting binary signals the theoretical ber is validated by the monte carlo simulation we find that the existence of time delay can change both the drift term and the diffusion coefficient in time delayed ffpe for small noise intensity the time delay extends the system response time and thus reduces the detection performance however effects of this kind will fade away with the increase of noise intensity

analytical and numerical investigations of the phase locked loop with time delay we derive the normal form for the delay induced hopf bifurcation in the first order phase locked loop with time delay by the multiple scaling method the resulting periodic orbit is confirmed by numerical simulations further detailed numerical investigations demonstrate exemplarily that this system reveals a rich dynamical behavior with phase portraits fourier analysis and lyapunov spectra it is possible to analyze the scaling properties of the control parameter in the period doubling scenario both qualitatively and quantitatively within the numerical accuracy there is evidence that the scaling constant of the time delayed phase locked loop coincides with the feigenbaum constant delta approximately 4 669 in one dimensional discrete systems

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 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

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

order parameters for class b lasers with a long time delayed feedback abstract a local dynamics for class b laser systems with optoelectronic feedback is considered in the case of a very long time delay we determine the conditions for the bifurcation of infinite dimension it is shown that the ordinary delay system can be described by a systematically derived complex ginzburg landau equation without delay terms the complicated quasi periodic dynamics near equilibrium can be demonstrated analytically on the basis of space time representation

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

an identity for bipartite matching and symmetric determinant abstract let a x aij x be an n n symmetric polynomial matrix in x and define a degx det a x the degree of the determinant of a x let g a be the associated bipartite graph the vertices of g a are identified with the rows and the columns of a and the edges with the nonzero entries of a we attach degx aij x to edge i j of g a as a weight and define gd 0 a to be the maximum weight of a perfect matching in g a then a gd 0 a and the equality holds in the generic case i e when the leading coefficients of aij x i j are independent parameters it is proven by a combinatorial argument that the gap between a and gd 0 a if any can be resolved by a unimodular congruence transformation that is for a nonsingular a x there exists a unimodular u x such that a x u x a x u x t satisfies a a gd 0 a note that if a x is transformed to a x u x a x u x t a remains invariant whereas gd 0 a does change since g a changes the proof relies on the dual integrality of bipartite matching polytopes well known in polyhedral combinatorics

an identity for matching and skew symmetric determinant let a aij be an n n skew symmetric matrix and g a be the associated graph the vertices of g a are identified with the rows and columns of a and the edges with the nonzero entries of a a basic fact used in tutte s 1947 paper on matching is det a 0 if and only if g a has a perfect matching this holds generically i e when the nonzero entries aij i j are independent parameters the present paper gives a weighted and nongeneric version of this relation let a x aij x be an n n skew symmetric polynomial matrix in x and define a degx det a x the degree of the determinant of a x we attach degx aij x to edge i j of g a as a weight and define gd a 2 maximum weight of a perfect matching in g a then a gd a with equality in the generic case it is proven by a combinatorial argument that the gap between a and gd a if any can be resolved by an unimodular congruence transformation that is for a nonsingular a x there exists a unimodular u x such that a x u x a x u x t satisfies a a gd a the proof relies on the dual integrality of perfect matching polytopes known in polyhedral combinatorics

the properties of the anti tumor model with coupling non gaussian noise and gaussian colored noise abstract the anti tumor model with correlation between multiplicative non gaussian noise and additive gaussian colored noise has been investigated in this paper the behaviors of the stationary probability distribution demonstrate that the multiplicative non gaussian noise plays a dual role in the development of tumor and an appropriate additive gaussian colored noise can lead to a minimum of the mean value of tumor cell population the mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states an increase in both the non gaussian noise intensity and the departure from the gaussian noise can accelerate the transition from the disease state to the healthy state on the contrary an increase in cross correlated degree will slow down the transition moreover the correlation time can enhance the stability of the disease state

effects of cross correlation on the relaxation time of a bistable system driven by cross correlated noise we study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross correlated noise using the projection operator method we derived an analytic expression for the relaxation time t c of the system which is the function of additive ensuremath alpha and multiplicative d noise intensities correlation intensity ensuremath lambda of noise and correlation time ensuremath tau of noise after introducing a noise intensity ratio and a dimensionless parameter r d ensuremath alpha and then performing numerical computations we find the following i for the case of rl1 the relaxation time t c increases as r increases ii for the cases of rg 1 there is a one peak structure on the t c ensuremath r plot and the effects of cross correlated noise on the relaxation time are very notable iii for the case of rl1 t c almost does not change with both ensuremath lambda and ensuremath tau and for the cases of rg 1 t c decreases as ensuremath lambda increases however t c increases as ensuremath tau increases ensuremath lambda and ensuremath tau play opposite roles in t c i e ensuremath lambda enhances the fluctuation decay of dynamical variable and ensuremath tau slows down the fluctuation decay of dynamical variable

delayed stochastic resonance with a 1 d ring abstract we study here a simple one dimensional ring composed of stochastic binary elements with delayed interaction with this model we can analytically compute interspike interval histograms and show how resonance or rhythmic behaviors arise with only noise and delay

combinatorial relaxation algorithm for mixed polynomial matrices the notion of mixed polynomial matrices is a mathematical tool for faithful description of discrete physical engineering dynamical systems it distinguishes two kinds of numbers fixed constants that account for conservation laws and independent parameters that represent physical characteristics

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

complex balancing motions of an inverted pendulum subject to delayed feedback control we show that an inverted pendulum that is balanced on a cart by linear delayed feedback control may exhibit small chaotic motion about the upside down position in periodic windows associated with this chaotic regime we find periodic orbits of arbitrarily high period that correspond to complex balancing motion of the pendulum with bounded velocity of the cart this result shows that complex balancing is possible in a controlled mechanical system with a geometric nonlinearity even when the control law is only linear this is in contrast to other proposed models that require a nonlinearity of the controller such as round off due to digitization we find the complex motion by studying homoclinic bifurcations of a reduced three dimensional vector field near a triple zero eigenvalue singularity more generally the dynamics we describe must be expected in any system with a triple zero singularity and reflection symmetry

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

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

retarded differential equations retarded differential equations rdes are differential equations having retarded arguments they arise in many realistic models of problems in science engineering and medicine where there is a time lag or after effect numerical techniques for such problems may be regarded as extensions of dense output methods for ordinary differential equations odes but scalar rdes are inherently infinite dimensional with a richer structure than their ode counterparts we give background material develop a theoretical foundation for the basic numerics and give some results not previously published