analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our 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

self gravitating nonlinear scalar fields we investigate the cauchy problem for the einstein scalar field equations in asymptotically flat spherically symmetric spacetimes in the standard 1 3 formulation we prove the local existence and uniqueness of solutions for initial data given on a space like hypersurface in the sobolev h1 h1 4 space solutions exist globally if a central integral singularity does not form and or outside an outgoing null hypersurface an explicit example demonstrates that there exists a local evolution with a naked initial curvature singularity at the symmetry centre

a regularity theorem for solutions of the spherically symmetric vlasov einstein system we show that if a solution of the spherically symmetric vlasov einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry the main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry

dynamics of stochastic delay lotka volterra systems with impulsive toxicant input and levy noise in polluted environments in this paper two stochastic delay lotka volterra systems i e competition system and predator prey system with impulsive toxicant input and levy noise in polluted environments are proposed and investigated under some simple assumptions sufficient and necessary criteria for stability in time average and extinction of each population are established the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended greatly

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

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

limit cycles for the competitive three dimensional lotka volterra system abstract in the first part of this paper it is proved that the number of limit cycles of the competitive three dimensional lotka volterra system in r 3 is finite if this system has not any heteroclinic polycycles in r 3 in the second part of this paper a 3d competitive lotka volterra system with two small parameters is discussed this system always has a heteroclinic polycycle with three saddles it is proved that there exists one parameter range in which the system is persistence and has at least two limit cycles and there exists other parameter ranges in which the system is not persistence and has at least one limit cycle

comparing stochastic lotka volterra predator prey models abstract the phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event in the present investigation we study this problem for three different stochastic models built from a single lotka volterra deterministic model more concretely we study their mean extinction time which satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence we can only compute numerical approximations we suggest a finite element method using freefem our analysis and numerical results allow us to conclude that there are important differences between the three models these differences enable us to choose the most natural way to turn a the deterministic model into a stochastic model

criteria for copositive matrices using simplices and barycentric coordinates abstract we present criteria for verifying the copositivity of an n n matrix given that all its principal submatrices of order n 1 are copositive for n 4 5 necessary and sufficient conditions for copositivity are given based on the sign distribution of the off diagonal elements of a single row here it is only assumed that one principal submatrix is copositive

periodic solution for a stochastic non autonomous competitive lotka volterra model in a polluted environment abstract in this paper we consider a stochastic non autonomous competitive lotka volterra model in a polluted environment we derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions furthermore we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution finally we make simulations to illustrate our analytical results

asymptotic behavior of a food chain model with stochastic perturbation abstract in this article asymptotic behavior of a stochastic food chain model is analyzed first of all we consider the dynamic of the deterministic system by analyzing the equilibria and their stability conditions then by lyapunov analysis methods we show that the system has a unique positive solution after that the stochastic stability and its long time behavior around the equilibriums of the deterministic system is given later we obtain the stochastic system and its corresponding deterministic system have similar properties when the white noise is small and then we show the conditions that there is a stationary distribution of the system which implies that the system is permanent at last we make simulations to verify the results of our analysis

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

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

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

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

stationary distribution and extinction of a stochastic ratio dependent predator prey system with stage structure for the predator abstract in this paper we deal with a stochastic predator prey model with stage structure for predator population and ratio dependent functional response the proposed mathematical model consists of a system of three stochastic differential equations to stimulate the interactions between prey population immature predator and mature predator population we first establish sufficient conditions for the existence and uniqueness of the positive solutions by constructing an appropriate lyapunov function then we extend the existence of stationary distribution under certain parametric restrictions we also obtain the sufficient conditions for extinction of the predator populations finally numerical simulations have been carried out to validate our analytical findings

stability in distribution of a stochastic predator prey system with s type distributed time delays abstract this paper concerns the dynamics of a stochastic predator prey lotka volterra system with s type distributed time delays sufficient conditions for the stability in distribution of the solutions sds to the system are obtained the results show that the dynamic scenarios of the sds are completely characterized by two parameters 1 2 among which 1 is just related to the environmental noise while 2 is closely related to both time delays and environmental noises if 2 0 then the distributions of prey predator converge weakly to a unique ergodic invariant distribution ueid if 1 0 2 then the predator goes to extinction while the distributions of prey converge weakly to a ueid if 0 1 then both the predator and prey go to extinction

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

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

global existence of generalized solutions of the spherically symmetric einstein scalar equations in the large in this paper we study the global initial value problem for the spherically symmetric einstein scalar field equations in the large we introduce the concept of a generalized solution of our problem and taking as initial hypersurface a future light cone with vertex at the center of symmetry we prove without any restriction on the size of the initial data the global in retarded time existence of generalized solutions

permanence of hybrid competitive lotka volterra system with levy noise abstract this paper concerns stochastic permanence of a hybrid competitive lotka volterra system with levy noise sufficient conditions of stochastic permanence are obtained by combining stochastic analytical techniques with m matrix analysis

the criteria for globally stable equilibrium in n dimensional lotka volterra systems abstract in this paper a set of sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium point in various submodels of the classic n dimensional lotka volterra system the submodels are the following systems competition cooperative or predator prey chain system and competition cooperative or predator prey model between one and multispecies the criteria in this paper are in explicit forms of the parameters and thus are easily verifiable

on the long time behavior of non autonomous lotka volterra models with diffusion via the sub supertrajectory method abstract in this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non autonomous lotka volterra systems in all the three cases of competition symbiosis or prey predator in particular under some conditions on the parameters we prove the existence of a unique nondegenerate global solution for these models which attracts any other complete bounded trajectory thus we generalize the existence of a unique strictly positive stable stationary solution from the autonomous case and we extend to lotka volterra systems the result for scalar logistic equations to this end we present the sub supertrajectory tool as a generalization of the now classical sub supersolution method in particular we also conclude pullback and forwards permanence for the above models

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing 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

kharitonov s theorem and bezoutians abstract an elementary proof of the kharitonov theorem is presented the proof is based on the concept of a bezoutian matrix generally exploiting the special structure of such matrices e g bezoutians toeplitz hankel or vandermonde matrices etc can be interesting e g leading to unified approaches in different cases as well as to further generalizations here the concept of the bezoutian matrix is used to provide a unified derivation of the kharitonov like theorems for the continuous time and discrete time settings finally the block anderson jury bezoutians are used to propose a possible technique to attack an difficult open problem related to the robust stability in the mimo case

a note on convex combinations of polynomials we show an equivalence between conditions for linear systems to be stabilizable by stable controllers and conditions for convex combinations of polynomials to be stable

wronskian based tests for stability of polynomial combinations in this paper a stability criterion based on counting the real roots of two specific polynomials is formulated to establish this result it is shown that a hyperbolicity condition and a strict positivity of a polynomial wronskian are necessary and sufficient for the stability of any real polynomial this result is extended to the stability study of some linear combinations of polynomials necessary and sufficient conditions of stability are obtained for polynomial segments and planes

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

permanence and asymptotic behaviors of stochastic predator prey system with markovian switching and levy noise abstract this paper concerns the dynamics of a stochastic predator prey system with markovian switching and levy noise first the existence and uniqueness of global positive solution to the system is proved then by combining stochastic analytical techniques with m matrix analysis sufficient conditions of stochastic permanence and extinction are obtained furthermore for the stochastic permanence case by means of four constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated finally our conclusions are illustrated through an example

an alternative proof of kharitonov s theorem an alternative proof is presented of kharitonov s theorem for real polynomials the proof shows that if an unstable root exists in the interval family then another unstable root must also show up in what is called the kharitonov plane which is delimited by the four kharitonov polynomials this fact is proved by using a simple lemma dealing with convex combinations of polynomials then a well known result is utilized to prove that when the four kharitonov polynomials are stable the kharitonov plane must also be stable and this contradiction proves the theorem

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

coexistence and exclusion of stochastic competitive lotka volterra models abstract this work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive lotka volterra model the conditions obtained are close to necessary in addition convergence in distribution of positive solutions of the model is also established a number of numerical examples are given to illustrate our results

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

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

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

asymptotic stability of a stochastic may mutualism system abstract this paper deals with a mutualism system in random environments in which the cooperation of two species is guaranteed depending on increasing the carrying capacity of each other mathematically we obtain the existence and uniqueness of a stable stationary distribution by means of markov semigroup theory and fokker planck equation in addition we prove that densities of the distributions for the solutions converge in l 1 to an invariant density under appropriate conditions numerical simulations are also presented to illustrate the theoretical results