文章研究了在污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响.通过构造~Lyapunov~函数,证明了系统全局正解的存在性;利用随机微分方程比较定理得到系统平均持续生存与灭绝的充分条件;应用~Has'minskii~定理证明了系统至少存在一个非平凡的正周期解,并给出了数值模拟.

This paper investigates the effects of impulsive toxicant input and psychological effect on stochastic predator-prey systems in a polluted environment. The authors firstly obtain that the system admits unique positive global solution starting from the positive initial value by choosing a suitable Lyapunov function. Then, by comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in mean are obtained. On the other hand, the authors prove that there exists at least one nontrivial positive periodic solution according to the theory of Has'minskii. Finally, some numerical simulations are introduced to illustrate the theoretical result.