parallel monte carlo simulations using a residence weight algorithm a parallel monte carlo mc algorithm the residence weight algorithm is proposed this algorithm is an extension to continuous ensembles of the residence time algorithm the proposed algorithm consists of generating several trial mc moves in parallel selecting one of them using appropriate relative probabilities and correcting the non boltzmannian sampling procedure by means of appropriate configuration weights the corresponding parallel boltzmannian scheme is based on a configurational bias monte carlo scheme and will also be considered the efficiency of both parallel algorithms has been compared in a case study the slow relaxation dynamics in a model silicate for a small number of trial moves generated in parallel we observe that the residence weight algorithm performs less efficiently than its corresponding configurational bias scheme by a factor of about 2 however when the number of parallel trial moves increases and becomes larger than ten we observe that the residence weight algorithm and the corresponding configurational bias scheme perform with equivalent efficiencies

dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

persistence and extinction in stochastic delay logistic equation by incorporating ornstein uhlenbeck process abstract the persistence and extinction pe are interesting topics in mathematics this research analyzed pe of stochastic logistic equations sle by incorporating the ornstein uhlenbeck process slop and stochastic delay logistic equation sdle by incorporating the ornstein uhlenbeck process sldop firstly we proved that slop and sldop have positive solutions likewise for stochastic permanence sp weak persistence in the mean wpm non persistence in the mean npm and extinction the sufficient conditions are established for slop and sldop subsequently for numerical simulation we used 4 stage stochastic runge kutta srk4 to illustrate the effectiveness of the results

new criteria on persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching abstract this paper concerns persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching by using some novel stochastic analysis techniques sufficient criteria for the partial permanence and partial extinction are established some novel sufficient conditions on persistence in mean and extinction are also obtained nontrivial examples are provided to illustrate our results

cyclical interactions with alliance specific heterogeneous invasion rates we study a six species lotka volterra type system on different two dimensional lattices when each species has two superior and two inferior partners the invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator prey pair whereby cyclic symmetries within the two three species defensive alliances are conserved monte carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance specific invasion rates this behavior is qualitatively reproduced by a four point mean field approximation the study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

existence and uniqueness theorems for periodic markov process and applications to stochastic functional differential equations abstract this work is devoted to an m valued markov process with a periodic transition probability function where m is a polish space sufficient conditions for the existence and uniqueness of the periodic markov process are given these existence theorems are rather general and the corresponding results in 1 11 15 23 are improved and generalized the uniqueness theorems for the periodic markov process are original as applications we study the existence uniqueness and global attractivity of periodic solution for the periodic stochastic n species lotka voltrra competitive model with bounded delays and the periodic stochastic neural networks with infinite delay respectively numerical simulations are presented to illustrate the main results

stability in distribution of neutral stochastic functional differential equations with markovian switching abstract stability in distribution of stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems there are several papers which study this stability for stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching technically in our paper we are concerned with the general neutral stochastic functional differential equations with markovian switching and we derive the sufficient conditions for stability in distribution at the end of our paper one example is established to illustrate the theory of our work

stochastic mutualism model under regime switching with levy jumps abstract this paper is concerned with a stochastic mutualism model under regime switching with levy jumps to begin with the existence and uniqueness of the global positive solution is proved with any given positive initial value then the sufficient conditions for stochastic permanence are established the critical value between extinction and persistence in mean is also obtained in addition under some suitable conditions we proved that there is a unique stationary distribution for the system without levy jumps our method relies on the lyapunov function analysis and the fredholm alternative the results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence

permanence and stability of a stage structured predator prey model abstract a predator prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey is proposed it is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predators do not have the ability to attack prey we obtain conditions that determine the permanence of the populations and the extinction of the populations furthermore we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model by exploiting the monotonicity of one equation of the model we obtain conditions for the global attractivity of the positive equilibrium which allow for long delay as long as the predator birth rate is large or the death rate of immature predators is small by constructing liapunov functionals we also obtain conditions under which the positive equilibrium is globally stable when the delay is small

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

dynamics of a stochastic cell to cell hiv 1 model with distributed delay abstract in this paper we consider a stochastic cell to cell hiv 1 model with distributed delay firstly we show that there is a global positive solution of this model before exploring its long time behavior then sufficient conditions for extinction of the disease are established moreover we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic lyapunov function the stationary distribution implies that the disease is persistent in the mean finally we provide some numerical examples to illustrate theoretical results

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

dynamics of a stochastic lotka volterra model perturbed by white noise abstract this paper continues the study of mao et al investigating two aspects of the equation d x t diag x 1 t x n t b a x t d t x t d w t t 0 the first of these is to slightly improve results in x mao s sabais e renshaw asymptotic behavior of stochastic lotka volterra model j math anal 287 2003 141 156 concerning with the upper growth rate of the total quantity i 1 n x i t of species by weakening hypotheses posed on the coefficients of the equation the second aspect is to investigate the lower growth rate of the positive solutions by using lyapunov function technique and using a changing time method we prove that the total quantity i 1 n x i t always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower growth rate

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

global observability of a class of nonlinear discrete time systems abstract it is shown that discrete time systems whose dynamics are governed by piecewise monotone maps of the interval are globally observable under a general class of observations the results rest on the fact that the dynamics are ergodic

sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching in this paper we prove that a stochastic logistic population under regime switching controlled by a markov chain is either stochastically permanent or extinctive and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions in the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems of the population model finally we illustrate our conclusions through two examples

a note on nonautonomous logistic equation with random perturbation abstract this paper discusses a randomized nonautonomous logistic equation d n t n t a t b t n t d t t d b t where b t is 1 dimensional standard brownian motion we show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

path sampling with stochastic dynamics some new algorithms we propose here some new sampling algorithms for path sampling in the case when stochastic dynamics are used in particular we present a new proposal function for equilibrium sampling of paths with a monte carlo dynamics the so called brownian tube proposal this proposal is based on the continuity of the dynamics with respect to the random forcing and generalizes all previous approaches when stochastic dynamics are used the efficiency of this proposal is demonstrated using some measure of decorrelation in path space we also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium in contrast with the usual jarzynski like switching this switching is very interesting to sample constrained paths starting from unconstrained paths or to perform simulated annealing in a rigorous way

qualitative analysis of a stochastic ratio dependent predator prey system a stochastic ratio dependent predator prey model is investigated in this paper by the comparison theorem of stochastic equations and ito s formula we obtain the global existence of a positive unique solution of the ratio dependent model besides a condition for species to be extinct is given and a persistent condition is established we also conclude that both the prey population and the ratio dependent function are stable in time average in the end numerical simulations are carried out to confirm our findings

permanence and extinction for a single species system with jump diffusion abstract in this study we consider the effect of jump diffusion random environmental perturbations on the permanence and extinction of a single species dispersal periodic system in poor patchy environments with the possibility of species loss during their dispersion among patches first we prove that there is a unique global positive solution to the system with any initial positive value with probability 1 and we obtain the sufficient conditions that stochastically ensure the ultimate boundedness as well as the asymptotic polynomial growth of the population system next we establish the sufficient conditions for the almost sure permanence in the mean stochastic permanence and extinction of the system in particular by constructing an appropriate integrating factor we obtain the sufficient conditions for the almost sure weak permanence of the patch the conditions obtained for permanence generalize the sufficient conditions established previously on the system without random environmental perturbations finally we discuss the biological implications of the main results

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

global observability of morse smale vectorfields abstract a procedure for investigating the global observability of a class of vectorfields is proposed the method derives from given qualitative properties of the flow it is shown that for morse smale flows local observability criteria can be tied together leading to a global theorem

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

computation of a chemical potential using a residence weight algorithm the test particle insertion method and its generalization to biased insertion schemes allows the computation of chemical potentials in fluids even though these techniques can be implemented in dense systems the convergence of the estimated value for the chemical potential must be carefully checked and additional simulations are actually required we propose to compute the chemical potential using a residence weight algorithm with this algorithm it is shown that for a given amount of computer time the degree of convergence towards the exact chemical potential correlates with the mean rate for accepting the trial particle insertions or deletions the residence weight algorithm thus offers a reliable built in tool for diagnosing the numerical convergence

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

observability of minimal distal systems in a recent series of papers drager and martin have shown global observability for a variety of particular classes of systems including both discrete and continuous time systems the underlying philosophy behind their methods is apparently that if a flow is ergodic and the system observation has a sufficiently special value the system is completely observable in this paper we prove observability for observed systems whose underlying flow is minimal and distal while our results hold also in discrete time we illustrate this result for invariant ergodic systems on nilmanifolds i e those invariant flows with an infinitesimal generator that is irrational modulo the commutator one well known example of such a flow is the irrational flow on a torus studied by drager and martin

the euler scheme for levy driven stochastic differential equations in relation with monte carlo methods to solve some integro differential equations we study the approximation problem of ee g x t by ee g bar x t n where x t 0 leq t leq t is the solution of a stochastic differential equation governed by a levy process z t bar x n t is defined by the euler discretization scheme with step fractn with appropriate assumptions we show that the error ee g x t ee g bar x t n can be expanded in powers of frac1n if the levy measure of z has finite moments of order high enough otherwise the rate of convergence is slower and its speed depends on the behavior of the tails of the levy measure the simulation of the increments of z t is also discussed

analysis on stochastic delay lotka volterra systems driven by levy noise abstract in this paper two types of stochastic lotka volterra systems i e competition system and predator prey system with time delays and levy noise are discussed for each model we establish sufficient and necessary criteria for stability in time average and extinction of each population the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended significantly these results point out that i time delays are harmless for stability in time average and extinction of our model ii both stability in time average and extinction have close relationships with levy noise iii the interaction rates play significant roles in determining the stability in time average and extinction of the populations

persistence and extinction in stochastic non autonomous logistic systems this paper studies two widely used stochastic non autonomous logistic models for the first system sufficient conditions for extinction non persistence in the mean weak persistence and stochastic permanence are established the critical number between weak persistence and extinction is obtained for the second system sufficient criteria for extinction non persistence in the mean weak persistence in the mean strong persistence in the mean and stochastic permanence are established the critical number between weak persistence in the mean and extinction is obtained it should be pointed out that this research is systematical and complete in fact the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper

free energy reconstruction from steered dynamics without post processing various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and by maximum likelihood post processing to reconstruct free energy landscapes here based on bayes theorem we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states the method is implemented with two steering schedules first using non autonomous steering we calculate the migration barrier of the vacancy in email protected second using an autonomous scheduling related to metadynamics and equivalent to temperature accelerated molecular dynamics we accurately reconstruct the two dimensional free energy landscape of the 38 atom lennard jones cluster as a function of an orientational bond order parameter and energy down to the solid solid structural transition temperature of the cluster and without maximum likelihood post processing

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

a stochastic sirs epidemic model with nonlinear incidence rate a stochastic sirs model with ratio dependent incidence rate is developed the global dynamics of the deterministic model is shown the stochastic dynamics of the sde model is given the existence of a unique stationary distribution of the sde model is displayed in this paper we investigate the global dynamics of a general sirs epidemic model with a ratio dependent incidence rate and its corresponding stochastic differential equation version for the deterministic model we show that the basic reproduction number r0 determines whether there is an endemic outbreak or not if r0 1 the disease persists for the stochastic model we show that its related reproduction number r0s can determine whether there is a unique disease free stationary distribution or a unique endemic stationary distribution in addition we provide analytic results regarding the stochastic boundedness and permanence extinction one of the most interesting findings is that random fluctuations introduced in our stochastic model can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

a remark on stochastic logistic model with diffusion stochastic logistic system with diffusion is proposed and studied almost sufficient and necessary conditions for stability in time average and extinction are established some numerical examples are introduced to support the main results

a remark on a stochastic logistic model with levy jumps this note is concerned with a famous stochastic logistic equation with levy noises sufficient and necessary conditions for extinction and permanence are established the results reveal that the levy noise may change the properties of population dynamics significantly the results also reveal an important property of the levy noise it is unfavorable for the permanence of the population some numerical simulations are introduced to validate the analytical results

analysis of a general stochastic non autonomous logistic model with delays and levy jumps abstract in this paper a general stochastic non autonomous logistic model with delays and levy jumps is proposed and studied sufficient criteria for extinction non persistence in the mean and weak persistence of the model are established the threshold between weak persistence and extinction is also obtained finally numerical simulations are introduced to illustrate the theoretical analysis results our results illustrate that both persistence and extinction have close relationships with time dependent delay and levy noise