具Markov转换和脉冲扰动的捕食-食饵系统的动力学

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

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.

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 longtime 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.