This paper considers an impulsive stochastic logistic model with infinite delay at the phase space $C_{g}$. Firstly, definition of solution to functional differential equation is established. Based on this definition, we show that our has a unique global positive solution. Then establish sufficient conditions for extinction, nonpersistence in mean, weak persistence and permanence The threshold between extinction obtained. In addition, effects perturbation are discussed, respectively....

This paper is concerned with a stochastic delay logistic model jumps. Sufficient and necessary conditions for extinction are obtained as well permanence. Numerical simulations introduced to support the theoretical analysis results. The results show that jump process can affect properties of population significantly, which conforms biological significance.

This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, the space $C_{g}$ as phase space, definition of solution to functional differential equation perturbation is established. According this definition, we show that our has an unique global positive solution. Then establish sufficient necessary conditions for extinction permanence model. In addition, effects on are discussed, respectively.

Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, permanence, global asymptotic stability are established. Moreover, threshold between persistence extinction obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.

The article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain significant criterion <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msubsup> <a:mrow> <a:mi>R</a:mi> </a:mrow> <a:mn>0</a:mn> <a:mi>S</a:mi> </a:msubsup> </a:math> relies on environmental noises. By means of Lyapunov function approach, show that there stationary distribution if <c:math...

This paper considers a stochastic Lotka-Volterra competitive model with infinite delay and impulsive perturbations. is new, more feasible accordance the actual. The aim to analyze what happens under With space $C_{g}$ as phase space, sufficient conditions for permanence in time average are established well extinction, stability global attractivity of each population. Numerical simulations also exhibited illustrate validity results this paper. In addition, knowledge given that statement [21]...

This paper considers a stochastic competitive system with distributed delay and general Lévy jumps. Almost sufficient necessary conditions for stability in time average extinction of each population are established under some assumptions. And two facts revealed: both have closer relationships the jumps, firstly; secondly, has no effect on system. Some simulation figures, which obtained by split-step <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This paper considers a stochastic Gilpin–Ayala model with jumps. First, we show the that has unique global positive solution. Then establish sufficient conditions for extinction, nonpersistence in mean, weak persistence, and permanence of The threshold between persistence extinction is obtained. Finally, make simulations to conform our analytical results. results jump process can change properties population significantly. Copyright © 2014 John Wiley & Sons, Ltd.