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1.
This paper considers a stochastic Gilpin–Ayala model with jumps. First, we show the model that has a unique global positive solution. Then we establish the sufficient conditions for extinction, nonpersistence in the mean, weak persistence, and stochastic permanence of the solution. The threshold between weak persistence and extinction is obtained. Finally, we make simulations to conform our analytical results. The results show that the jump process can change the properties of the population model significantly. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

2.
In this article, an impulsive stochastic tumor-immune model with regime switching is formulated and explored. Firstly, it is proven that the model has a unique global positive solution. Then sufficient criteria for extinction, non-persistence in the mean, weak persistence and stochastic permanence are provided. The threshold value between extinction and weak persistence is gained. In addition, the lower- and the upper-growth rates of tumor cells are estimated. The results demonstrate that the dynamics of the model are intimately associated with the random perturbations and impulsive perturbations. Finally, biological implications of the results are addressed with the help of real data and numerical simulations.  相似文献   

3.
This is a continuation of our paper [M. Liu, K. Wang, X. Liu. Long term behaviors of stochastic single-species growth models in a polluted environment. Appl Math Model 2011;35:752–62]. This work still devotes to studying three stochastic single-species models in a polluted environment. For the first system, sufficient criteria for extinction, stochastic non-persistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the population are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. For the second model, sufficient conditions for extinction, stochastic non-persistence in the mean, stochastic weak persistence, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is derived. For the third system, the threshold between stochastic weak persistence and extinction is obtained.  相似文献   

4.
In this paper, a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. For this model, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The influences of the stochastic noises to the properties of the stochastic model are discussed. The property permanence for the model is preserved with the sufficiently small noise and sufficiently large noise may cause extinction of the model. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.  相似文献   

5.
A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.  相似文献   

6.
A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.  相似文献   

7.
Taking both white noises and colored noises into account, a stochastic single-species model with Markov switching and impulsive toxicant input in a polluted environment is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Some simulation figures are introduced to illustrate the main results.  相似文献   

8.
A stochastic logistic model under regime switching is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Then we show that this threshold also is the threshold between stochastic permanence and extinction under a simple additional condition. The results show that firstly, the stationary probability distribution of the Markov chain plays a key role in determining the permanence and extinction of the population. Secondly, different types of environmental noises have different effects on the permanence and extinction of the population. Thirdly, the more the stochastic noises, the easier the population goes to extinction.  相似文献   

9.
主要是讨论了一类具有变时滞的随机logi8tic种群系统.首先探讨了系统全局正解的存在性;然后获得了系统弱持久性和灭绝性的充分条件,获得了种群系统弱持续生存与灭绝之间的临界值.  相似文献   

10.
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.  相似文献   

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