具Markov转换和脉冲扰动的捕食-食饵系统的动力学

数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 569-583.

具Markov转换和脉冲扰动的捕食-食饵系统的动力学

张树文

集美大学理学院福建厦门 361021

收稿日期:2015-10-08 修回日期:2016-03-15 出版日期:2016-06-26 发布日期:2016-06-26
作者简介:张树文,anzsw_123@163.com
基金资助:
国家自然科学基金（31272653，11301216）和福建省自然科学基金（2016J01667）资助

Dynamics of a Predator-Prey System with Impulsive Perturbations and Markovian Switching

Zhang Shuwen

College of Science, Jimei University, Fujian Xiamen 361021

Received:2015-10-08 Revised:2016-03-15 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (31272653, 11301216) and Fujian Provincial Science Foundation (2016J01667)

摘要/Abstract

摘要：

该文研究一个具有Markov转换和脉冲扰动的随机时滞捕食-食饵系统. 首先确定系统存在唯一全局正解并给出系统解的均值上极限的估计；其次获得了系统解轨道长时间的渐近行为和系统的随机最终有界性；进而构造合适的Lyapunov函数并使用随机微分方程的比较定理，给出种群灭绝、平均非持续生存的充分条件；最后，给出简短的结论.

关键词: 捕食-食饵模型, 随机扰动, 脉冲效应, 灭绝, 平均非持续生存

Abstract:

In this paper, a stochastic delay predator-prey system with Markovian switching and impulsive perturbations is studied. We establish conditions for the existence of a global positive solution for the considered system. The superior limit of expectations for the solution of this system is estimated. Afterwards we obtain certain asymptotic results regarding long-time behavior of trajectories of the solution and prove stochastically ultimately boundedness of the system. Furthermore, by constructing a suitable Lyapunov function and using comparison theorem of stochastic differential equation, a set of sufficient conditions for extinction, non-persistence in the mean for every positive solution of the system are obtained. Finally, we give the conclusion.

Key words: Predator-prey system, Stochastic perturbations, Impulsive effects, Extinction, Non-persistence in the mean

中图分类号:

O231

张树文. 具Markov转换和脉冲扰动的捕食-食饵系统的动力学[J]. 数学物理学报, 2016, 36(3): 569-583.

Zhang Shuwen. Dynamics of a Predator-Prey System with Impulsive Perturbations and Markovian Switching[J]. Acta mathematica scientia,Series A, 2016, 36(3): 569-583.

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