具Markov转换和脉冲扰动的捕食-食饵系统的动力学

Abstract

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

CLC Number:

O231

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

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