how colored environmental noise affects population extinction environmental noise can cause an exponential reduction in the mean time to extinction mte of an isolated population we study this effect on an example of a stochastic birth death process with rates modulated by a colored that is correlated gaussian noise a path integral formulation yields a transparent way of evaluating the mte and finding the optimal realization of the environmental noise that determines the most probable path to extinction the population size dependence of the mte changes from exponential in the absence of the environmental noise to a power law for a short correlated noise and to no dependence for long correlated noise we also establish the validity domains of the white noise limit and adiabatic limit

uniform positivity improving property sobolev inequalities and spectral gaps abstract we introduce a certain kind of strong ergodicity condition to study the existence of spectral gap for markov generator we can estimate the spectral gap using the ergodicity condition and a sobolev type inequality we apply our results to the dirichlet form on wiener spaces riemannian manifolds and loop spaces

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

estimation of the first eigenvalue of second order elliptic operators this note studies the first non trivial eigenvalue of second order self adjoint elliptic operators in rd some lower bounds of the eigenvalue are obtained by using a probabilistic approach and some geometric consideration in one dimensional case an analytic proof is also presented the resulting bounds can be sharp

holomorphic dirichlet forms on complex manifolds a complete description of all holomorphic dirichlet forms on complex hyperbolic space is given they are classified in terms of the lie algebra of the automorphism group which we take to act in the unit ball of n we show that the measure defining the holomorphic dirichlet form is finite if and only if the real part of the associated holomorphic vector field points outward at the boundary of the unit ball a logarithmic sobolev inequality is proven to hold whenever this measure is finite all holomorphic dirichlet forms over complex hyperbolic space complex projective space and n are now known

signatures of noise enhanced stability in metastable states the lifetime of a metastable state in the transient dynamics of an overdamped brownian particle is analyzed both in terms of the mean first passage time and by means of the mean growth rate coefficient both quantities feature nonmonotonic behaviors as a function of the noise intensity and are independent signatures of the noise enhanced stability effect they can therefore be alternatively used to evaluate and estimate the presence of this phenomenon which characterizes metastability in nonlinear physical systems

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model

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

role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials we present a study of the noise driven escape of an overdamped brownian particle moving in a cubic potential profile with a metastable state we analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials we observe the noise enhanced stability effect for all the initial unstable states investigated for a fixed potential we find a peculiar initial condition xc which separates the set of the initial unstable states in two regions those which give rise to divergences from those which show nonmonotonic behavior of the average escape time for fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time

levy brownian motion on finite intervals mean first passage time analysis we present the analysis of the first passage time problem on a finite interval for the generalized wiener process that is driven by levy stable noises the complexity of the first passage time statistics mean first passage time cumulative first passage time distribution is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non gaussian noises the validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2 recovering in this limit the standard results for the fokker planck dynamics driven by gaussian white noise

rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations abstract the long time limit behavior of the stochastic lotka volterra model of a symbiotic metapopulation subjected to generalized verhulst self regulation is considered the influence of a time variable environment on the carrying capacities of subpopulations is modeled as a periodic deterministic part and a symmetric dichotomous noise relying on the mean field approach it is established that at certain parameter regimes the mean field average subpopulations size exhibits hysteresis in respect to the noise correlation time manifested in the appearance of colored noise induced discontinuous transitions especially it is shown that the relative fluctuation of the subpopulation sizes exhibits accelerated increase prior to abrupt transitions of the metapopulation state moreover in certain cases the autocorrelation function of the population sizes demonstrates anticorrelation at some values of the lag time

first passage and arrival time densities for levy flights and the failure of the method of images we discuss the first passage time problem in the semi infinite interval for homogeneous stochastic markov processes with levy stable jump length distributions x l x 1 x l namely levy flights lfs in particular we demonstrate that the method of images leads to a result which violates a theorem due to sparre andersen according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density fptd governed by the universal long time decay t 3 2 conversely we show that for lfs the direct definition known from gaussian processes in fact defines the probability density of first arrival which for lfs differs from the fptd our findings are corroborated by numerical results

mean escape time in a system with stochastic volatility we study the mean escape time in a market model with stochastic volatility the process followed by the volatility is the cox ingersoll and ross process which is widely used to model stock price fluctuations the market model can be considered as a generalization of the heston model where the geometric brownian motion is replaced by a random walk in the presence of a cubic nonlinearity we investigate the statistical properties of the escape time of the returns from a given interval as a function of the three parameters of the model we find that the noise can have a stabilizing effect on the system as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious brownian particle we compare the probability density function of the return escape times of the model with those obtained from real market data we find that they fit very well

log sobolev inequality on non convex riemannian manifolds abstract counterexamples are constructed to show that when the second fundamental form of the boundary is bounded below by a negative constant any curvature lower bound is not enough to imply the log sobolev inequality this indicates that in the study of functional inequalities on non convex manifolds the concavity of the boundary cannot be compensated by the positivity of the curvature next when the boundary is merely concave on a bounded domain a criterion on the log sobolev inequality known for convex manifolds is proved finally when the concave part of the boundary is unbounded a sobolev inequality for a weighted volume measure is established which implies an explicit sufficient condition for the log sobolev inequality to hold on non convex manifolds

functional inequalities on arbitrary riemannian manifolds abstract for any connected not necessarily complete riemannian manifold we construct a probability measure of type e v x d x where d x is the riemannian volume measure and v is a function c smooth outside a closed set of zero volume satisfying poincare sobolev type functional inequalities in particular v is c smooth on the whole manifold when the poincare and the super poincare inequalities are considered the sobolev inequality for infinite measures are also studied

kinetics of self induced aggregation of brownian particles non markovian and non gaussian features in this paper we have explored a model for self induced aggregation of brownian particles incorporating non markovian and non gaussian character of the associated random noise processes the time evolution of each individual is guided by an overdamped langevin equation of motion with a nonlocal drift arising out of the imbalance in the local distribution of the other individuals our simulation results show that colored noise enhances the tendency of cluster formation another observation is that the critical noise variance decreases at first with increase in noise correlation time followed by an increase after exhibiting a minimum furthermore in the long time limit the cluster number in the aggregation process exhibits depletion with time following a power law with an exponent which increases remarkably with non markovian character of the noise processes

asymptotics of sample entropy production rate for stochastic differential equations using the dimension free harnack inequality and the integration by parts formula for the associated diffusion semigroup we prove the central limit theorem the moderate deviation principle and the logarithmic iteration law for the sample entropy production rate of a family of stochastic differential equations

detection of noise corrupted sinusoidal signals with josephson junctions we investigate the possibility of exploiting the speed and low noise features of josephson junctions for detecting sinusoidal signals masked by gaussian noise we show that the escape time from the static locked state of a josephson junction is very sensitive to a small periodic signal embedded in the noise and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component we propose and characterize two detection strategies in the first the initial phase is supposedly unknown incoherent strategy while in the second the signal phase remains unknown but is fixed coherent strategy our proposals are both suboptimal with the linear filter being the optimal detection strategy but they present some remarkable features such as resonant activation that make detection through josephson junctions appealing in some special cases

escape driven by α stable white noises we explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the brownian particle is driven by white levy noise in a dynamical regime where inertial effects can safely be neglected the behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise induced discontinuity which is caused by the generalized brownian paths that jump beyond the barrier location without actually hitting it this fact implies that the boundary conditions for the mean first passage time mfpt are no longer determined by the well known local boundary conditions that characterize the case with normal diffusion by numerically implementing properly the set up boundary conditions we investigate the survival probability and the average escape time as a function of the corresponding levy white noise parameters depending on the value of the skewness beta of the levy noise the escape can either become enhanced or suppressed a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of levy noise exhibiting a marked discontinuity at alpha 1 we find that the typical factor of 2 that characterizes for normal diffusion the ratio between the mfpt for well bottom to well bottom and well bottom to barrier top no longer holds true for sufficiently high barriers the survival probabilities assume an exponential behavior versus time distinct non exponential deviations occur however for low barrier heights

logarithmic sobolev inequalities on noncompact riemannian manifolds this paper presents a dimension free harnack type inequality for heat semigroups on manifolds from which a dimension free lower bound is obtained for the logarithmic sobolev constant on compact manifolds and a new criterion is proved for the logarithmic sobolev inequalities abbrev lsi on noncompact manifolds as a result it is shown that lsi may hold even though the curvature of the operator is negative everywhere

estimation of spectral gap for elliptic operators a variational formula for the lower bound of the spectral gap of an elliptic operator is presented in the paper for the first time the main known results are either recovered or improved a large number of new examples with sharp estimate are illustrated moreover as an application of the march coupling the poincare inequality with respect to the absolute distribution of the process is also studied

levy flights in a steep potential well levy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs chechkin et al phys rev e 67 010102 r 2003 in this paper we present a detailed study of levy flights in potentials of the type u x x c with c 2 apart from the bifurcation into bimodality we find the interesting result that for c 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial condition and the building up of the two emerging side peaks which are characteristic for the stationary state thus for certain system parameters there exists a transient trimodal distribution of the levy flight these properties of levy flights in external potentials of the power law type can be represented by certain phase diagrams we also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process

influence of noise on the synchronization of the stochastic kuramoto model we consider the kuramoto model of globally coupled phase oscillators subject to ornstein uhlenbeck and non gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process we use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise and find that the threshold of synchronization strongly depends on the nature of the noise it is found to be lower for both the ornstein uhlenbeck and non gaussian processes compared to the case of white noise a finite correlation time also favors the achievement of the full synchronization of the system in contract to the white noise process which does not allow that finally we discuss possible applications of the stochastic kuramoto model to oscillations taking place in biochemical systems

when noise decreases deterministic diffusion dynamical noise acting homogeneously in each time step can enhance the stability of an unstable fixed point however if dynamical noise is added locally in state space additional clear enhancement can be achieved if this restriction is chosen properly a systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented and optimal parameters for the stabilizing mechanisms are discussed as a consequence it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models

a large deviation analysis on the near equivalence between external and internal reservoirs within the spirit of van kampen s langevin approach we discuss the limits of validity of rephrasing the non equilibrium problem of a particle subject to an external work reservoir a system where the fluctuation dissipation relation is not verified into the simpler case with an internal heat reservoir for which the fluctuations and the dissipation arise from the same source using a convenient mapping of the thermomechanical parameters we show that counter intuitively such approach is not only valid for steady state time independent quantities but also for time dependent thermostatistical quantities namely the injected and dissipated fluxes we connect this result with the problem of large deviations and conclude that in this context we can only distinguish reservoirs by analysing the fluctuations of accumulated fluctuations as a by product we learn that the best reference approximation to the large deviation functions of a non markovian external reservoir system is not the respective internal reservoir limit as often assumed and suggested by the langevin approach but its internal reservoir analogue system obtained from the mapping of the original thermomechanical parameters

escape times in fluctuating metastable potential and acceleration of diffusion in periodic fluctuating potentials abstract the problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered for the overdamped brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first passage time as a function of the potential parameters the noise intensity and the mean rate of switchings of the dichotomous noise we find noise enhanced stability phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed for the diffusion of the overdamped brownian particle in a fast fluctuating symmetric periodic potential we obtain that the effective diffusion coefficient depends on the mean first passage time as discovered for fixed periodic potential the effective diffusion coefficients for sawtooth sinusoidal and piecewise parabolic potentials are calculated in closed analytical form

efficient evaluation of neuron populations receiving colored noise current based on a refractory density method the expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential for the case of colored noise we propose this approximation in order to extend the recently proposed white noise model a v chizhov and l j graham phys rev e 75 011924 2007 to the case of colored noise applying a refractory density approach to conductance based neurons the uncoupled neurons of a single population receive a common input and are dispersed by the noise within the framework of the model the effect of noise is expressed by the so called hazard function which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term to derive the hazard function we solve the kolmogorov fokker planck equation for a mean voltage driven neuron fluctuating due to colored noisy current we show that a sum of both a self similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case we demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate and fire and detailed conductance based neurons in response to an injected current step

application of coupling methods to the neumann eigenvalue problem by using coupling methods some lower bounds are obtained for the first neumann eigenvalue on riemannian manifolds this method is new and the results improve some known estimates an example shows that our estimates can be sharp

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

levy flights transitions and meta stability we consider l vy flights of stability index 0 2 in a potential landscape in the limit of a small noise parameter we give a purely probabilistic description of the random dynamics on the basis of a special decomposition of the driving l vy processes into independent small jumps and compound poisson parts we prove that escape times from a potential well are exponentially distributed and their mean values increase as a power of the noise intensity this allows us to obtain meta stability results for a jump diffusion in a double well potential

noise intensity fluctuation in langevin model and its higher order fokker planck equation abstract in this paper we investigate a langevin model subjected to stochastic intensity noise sin which incorporates temporal fluctuations in noise intensity we derive a higher order fokker planck equation hfpe of the system taking into account the effect of sin by the adiabatic elimination technique stationary distributions of the hfpe are calculated by using the perturbation expansion we investigate the effect of sin in three cases a parabolic and quartic bistable potentials with additive noise b a quartic potential with multiplicative noise and c a stochastic gene expression model we find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal to trimodal transition in probability distributions these results are validated with monte carlo simulations

isotype submodules of p local balanced projective groups by giving necessary and sufficient conditions for two isotype submodules of a p local balanced projective group to be equivalent we are able to introduce a general theory of isotype submodules of p local balanced projective groups or ib modules numerous applications of the above result are available particularly for the special class of ib modules introduced by wick known as skt modules we first show that the class of skt modules is closed under direct summands and then we are able to show that if h appears as an isotype submodule of the p local balanced projective group g such that g h is the coproduct of countably generated torsion groups then h is an skt module finally we show that ib modules satisfy general structural properties such as transitivity full transitivity and the equivalence of p high

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

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account we study the causes of noise delayed decay of unstable states in nonlinear dynamic systems within the framework of the overdamped brownian motion model for the analysis we use the exact expressions for the decay times of unstable states which take into account the inverse probability current in contrast to the well known mean first passage time method these expressions are valid for any intensity of fluctuations and for arbitrary potential profiles the effect of delay is shown to arise under the decay of unstable nonequilibrium states due to the action of two different mechanisms these mechanisms are caused by the inverse probability current and by the nonlinearity of potential describing an unstable state

on logarithmic sobolev constant for diffusion semigroups abstract this paper is concerned with estimates for the constant in the logarithmic sobolev inequality as an application we show that for the laguerre semigroup with the generator xd 2 x d the logarithmic sobolev constant satisfies log 3 6 log 3 16 log 3 6 for 0 1 2 and 4 for 1 2

cancellation phenomenon of barrier escape driven by a non gaussian noise the levy noise with a long tail distribution induced particle escape from a metastable potential is shown to display a feature called a cancellation phenomenon as compared to the brownian motion case as a consequence the escape rate is found to be a nonmonotonous function of the levy index mu and the arrhenius law is not obeyed we have also derived a rate expression using the reactive flux method which supports our numerical findings namely with the decrease of mu a large positive flow is allowed to establish at the barrier however the probability passing over the saddle point decreases this implies that the particles outside the barrier come back to the inside and cancel with themselves

resonant activation in a bistable system the analog simulation of an overdamped brownian particle in a quartic double well potential driven by an external either gaussian or dichotomic multiplicative noise is performed with special focus on the phenomenon of resonant activation such an effect is shown to occur on increasing the correlation time of the multiplicative noise while keeping the noise variance constant the asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated simple qualitative arguments are produced to justify the results thus obtained furthermore the traversal barrier that is the effective barrier at the time the system switches state is shown to have a minimum for a certain value of the noise correlation time though not always in coincidence with the relevant resonant activation value textcopyright 1996 the american physical society

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

escape rate of levy particles from truncated confined and unconfined potentials abstract for a double well potential consisting of a truncated quartic potential and a truncated harmonic potential the inter well escape rates of levy particles are investigated numerically and analytically for the cauchy case with focus on the former the escape rate of levy particles from the truncated confined quartic potential well possesses qualitatively different characteristics compared with that from the truncated harmonic potential well as reflected in the noise intensity dependence and levy index dependence of the escape rate two kinds of different escape mechanisms exist for low noise and high noise intensities as the noise intensity increases the escaping particles in quasi stationary state present a noise induced phase transition phenomenon wherein the distribution of levy particles transits from a bimodal narrow distribution to a unimodal wide distribution the characteristics of the escape rate in low and high noise intensities can be understood by the distributions of levy particles and the features of levy noise

trichotomous noise controlled signal amplification in a generalized verhulst model abstract the long time limit of the probability distribution and statistical moments for a population size are studied by means of a stochastic growth model with generalized verhulst self regulation the effect of variable environment on the carrying capacity of a population is modeled by a multiplicative three level markovian noise and by a time periodic deterministic component exact expressions for the moments of the population size have been calculated it is shown that an interplay of a small periodic forcing and colored noise can cause large oscillations of the mean population size the conditions for the appearance of such a phenomenon are found and illustrated by graphs implications of the results on models of symbiotic metapopulations are also discussed particularly it is demonstrated that the effect of noise generated amplification of an input signal gets more pronounced as the intensity of symbiotic interaction increases

bifurcation bimodality and finite variance in confined levy flights we investigate the statistical behavior of levy flights confined in a symmetric quartic potential well u x proportional variant x 4 at stationarity the probability density function features a distinct bimodal shape and decays with power law tails which are steep enough to give rise to a finite variance in contrast to free levy flights from a delta initial condition a bifurcation of the unimodal state is observed at t c 0 the nonlinear oscillator with potential u x ax 2 2 bx 4 4 a b 0 shows a crossover from unimodal to bimodal behavior at stationarity depending on the ratio a b

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

on estimation of the logarithmic sobolev constant and gradient estimates of heat semigroups this paper presents some explicit lower bound estimates of logarithmic sobolev constant for diffusion processes on a compact riemannian manifold with negative ricci curvature let ric k for some k 0 and d d be respectively the dimension and the diameter of the manifold if the boundary of the manifold is either empty or convex then the logarithmic sobolev constant for brownian motion is not less than

on endomorphism rings of non separable abelian p groups there have been spectacular advances in recent years in the so called realization problem for certain classes of abelian groups and modules the advances have derived mainly from powerful combinatorial set theoretic tools pioneered by shelah in the case of separable abelian p groups these results appear e g in 1 4 51 for non separable abelian p groups the most significant contribution has been 2 our objective in this paper is to extend the results in 2 and derive analogous results to those obtained in 4 51 it is perhaps worth pointing out that our methods are entirely algebraic the necessary set theoretical work has been carried out in the separable case and no further set theoretical arguments are needed in this the work is reminiscent of s all our set theory with one exception is in zfc and this is not acknowledged in the statement of individual results in the exceptional case where we work in godel s constructible universe v l this is acknowledged by appending v l after the statement number the principal realization result can be stated as

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

linear and nonlinear experimental regimes of stochastic resonance we investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode the experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude we observe both a regime described by the linear response theory and the nonlinear deviation from it in the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density when these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input

positive lyapunov exponents in the kramers oscillator the maximum lyapunov exponent is computed numerically for the double well oscillator in a heat bath positive exponents are found in a wide range of friction coefficients in the low damping regime

concept of complexity in random dynamical systems we introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system in dynamical systems with small random perturbations this indicator coincides with the rate k of divergence of nearby trajectories evolving under two different noise realizations the meaning of k is discussed in the context of the information theory and it is shown that it can be determined from real experimental data in the presence of strong dynamical intermittency the value of k is very different from the standard lyapunov exponent ensuremath lambda mathrm ensuremath sigma computed considering two nearby trajectories evolving under the same realization of the randomness however the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models textcopyright 1996 the american physical society

the transitivity of local warfield groups abstract for a fixed prime p let g denote a module over the integers localized at p such a module is often referred to as a p local abelian group following established precedent we say that g is transitive provided that there exists an automorphism of g that maps a onto b whenever a and b are elements of g having the same height sequence however relatively few nontorsion g meet this criterion of transitivity indeed as we show there are four different classes of simply presented p local groups of torsion free rank 3 that are nontransitive in this article we introduce a weaker version of transitivity that allows all local warfield groups summands of simply presented p local groups to qualify as being transitive in this connection we associate with each element of a local warfield group g a new invariant called a type vector and we prove that there is an automorphism of g that maps a onto b if and only if a and b have the same height sequence and the same type vector as an application of this result we are able to determine exactly which local warfield groups are transitive in the classical sense also our results yield an alternate proof of a recent result of files regarding the equivalence of transitivity and full transitivity for local warfield groups finally we give a complete survey of transitivity for local warfield groups of torsion free rank 3

harnack inequalities for log sobolev functions and estimates of log sobolev constants by using the maximum principle and analysis of heat semigroups harnack inequalities are studied for log soboley functions from this some lower bound estimates of the log soboley constant are presented by using the spectral gap inequality and the coupling method the resulting inequalities either recover or improve the corresponding ones proved by chung and yau especially harnack inequalities and estimates of log sobolev constants can be dimension free

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

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

roles of capital flow on the stability of a market system abstract the roles of capital flow in an ensemble composed of sub markets are investigated a modified heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble respectively the mean escape times of two sub markets with a cubic nonlinearity are calculated by using numerical simulation the results evidence that i there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when 0 denotes strength of correlation between two wiener processes of the stock price and the volatility ii when 0 the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow but monotonously strengthened by delay time of capital outflow

statistics of a leaky integrate and fire model of neurons driven by dichotomous noise the behavior of a stochastic leaky integrate and fire model of neurons is considered the effect of temporally correlated random neuronal input is modeled as a colored two level dichotomous markovian noise relying on the riemann method exact expressions for the output interspike interval density and for the serial correlation coefficient are derived and their dependence on noise parameters such as correlation time and amplitude is analyzed particularly noise induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established the features of spike statistics analytically revealed in our study are compared with recently obtained results for a perfect integrate and fire neuron model

the state variable correlation function of the bistable system subject to the cross correlated noises abstract the effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross correlated noises were studied applying an approximate fokker planck equation to the system the analytic expression for the state variable correlation function of the system is derived by projection operator method from numerical computations we find that the normalized correlation function c s decreases exponentially as the decay time s increases and decreases with increasing cross correlated strength however c s increases with increasing cross correlated time and play opposing roles in the c i e enhances the rate of fluctuation decay of dynamical variable and the slows down the rate of fluctuation decay of dynamical variable

resonant activation in piecewise linear asymmetric potentials this work analyzes numerically the role played by the asymmetry of a piecewise linear potential in the presence of both a gaussian white noise and a dichotomous noise on the resonant activation phenomenon the features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum from the initial well to the bottom of the adjacent potential well because of the asymmetry of the potential profile together with the random external force uniform in space we find for the different asymmetries 1 an inversion of the curves of the mean first passage time in the resonant region of the correlation time of the dichotomous noise for low thermal noise intensities 2 a maximum of the mean velocity of the brownian particle as a function of and 3 an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated an inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise behavior confirmed by recent experiments

leapover lengths and first passage time statistics for levy flights exact results for the first passage time and leapover statistics of symmetric and one sided levy flights lfs are derived lfs with a stable index alpha are shown to have leapover lengths that are asymptotically power law distributed with an index alpha for one sided lfs and surprisingly with an index alpha 2 for symmetric lfs the first passage time distribution scales like a power law with an index 1 2 as required by the sparre andersen theorem for symmetric lfs whereas one sided lfs have a narrow distribution of first passage times the exact analytic results are confirmed by extensive simulations

stability properties of nonhyperbolic chaotic attractors with respect to noise we study local and global stability of nonhyperbolic chaotic attractors contaminated by noise the former is given by the maximum distance of a noisy trajectory from the noisefree attractor while the latter is provided by the minimal escape energy necessary to leave the basin of attraction calculated with the hamiltonian theory of large fluctuations we establish the important and counterintuitive result that both concepts may be opposed to each other even when one attractor is globally more stable than another one it can be locally less stable our results are exemplified with the holmes map for two different sets of parameter and with a juxtaposition of the holmes and the ikeda maps finally the experimental relevance of these findings is pointed out

statistics of residence time for levy flights in unstable parabolic potentials we analyze the residence time problem for an arbitrary markovian process describing nonlinear systems without a steady state we obtain exact analytical results for the statistical characteristics of the residence time for diffusion in a fully unstable potential profile in the presence of levy noise we get the conditional probability density of the particle position and the average residence time the noise enhanced stability phenomenon is observed in the system investigated results from numerical simulations are in very good agreement with analytical ones

noise enhanced stability in fluctuating metastable states we derive general equations for the nonlinear relaxation time of brownian diffusion in randomly switching potential with a sink for piece wise linear dichotomously fluctuating potential with metastable state we obtain the exact average lifetime as a function of the potential parameters and the noise intensity our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential we find noise enhanced stability phenomenon in the system investigated the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise we obtain the parameter region of the fluctuating potential where the effect can be observed the system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential

axiom 3 modules by introducing the concept of a knice submodule a refinement of the notion of nice subgroup we are able to formulate a version of the third axiom of countability appropriate to the study of plocal mixed groups in the spirit of the well known characterization of totally projective pgroups our axiom 3 modules in fact form a class of zp modules encompassing the totally projectives in the torsion case for which we prove a uniqueness theorem and establish closure under direct summands indeed axiom 3 modules turn out to be precisely the previously classified warfield modules but with the added power of the third axiom of countability characterization we derive numerous new results including the resolution of a long standing problem of warfield and theorems in the vein of familiar criteria due to kulikov and pontryagin

estimates of logarithmic sobolev constant an improvement of bakry emery criterion this paper is mainly devoted to estimate the logarithmic sobolev abbrev l s constant for diffusion operators on manifold or in rd in most cases we study the lower bounds but a generalization to a korzeniowski j funct anal 71 1987 363 370 theorem 1 for the upper bound is also presented theorem 1 5 based on a simple observation due to j d deuschel and d w stroock j funct anal 92 1990 30 48 of the comparison between the l s constants for different potentials the powerful bakry emery criterion for the l s inequality is improved considerably in the paper especially for the manifolds with non positive sectional curvatures theorem 1 3 1 in terms of our notation r inf x p r infx tx m x 1 ricc hessv x x where x p is the distance betweenxand an arbitrary fixed pointp m the improvement can be roughly stated as follows the condition infr 0 r 0 for which the criterion is available is now replaced by supr 0 r 0