中文摘要：

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食-食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.

英文摘要：

A predator-prey model was considered,in which both the predators and the preys dispersed among n patches under stochastic perturbations.Based on the method of Lyapunov functions,it was proved that a unique global positive solution existed for any given positive initial value;in turn,the property of ultimate boundedness was obtained.In addition,the sufficient conditions for the extinctions of the preys and even the whole system were given.Finally,the theoretic conclusions were validated by numerical simulations.