捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析  

Dynamics of Dual-Dispersal Predator-Prey Systems Under Stochastic Perturbations

作　　者：祖力[1] 黄冬冬[1] 柳扬[2] 

机构地区：[1]海南师范大学数学与统计学院,海口571158 [2]大连大学信息工程学院,辽宁大连116600

出　　处：《应用数学和力学》2017年第3期355-368,共14页Applied Mathematics and Mechanics

基　　金：海南省教育厅高等学校科学研究项目(Hjkj2013-16);海南省自然科学基金(20161006)

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.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.

关 键 词：捕食-食饵模型 随机扰动 扩散 随机最终有界 灭绝性 

分 类 号：O175.1[理学—数学]