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.
出处
《应用数学和力学》
CSCD
北大核心
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)
关键词
捕食-食饵模型
随机扰动
扩散
随机最终有界
灭绝性
predator-prey model
stochastic perturbation
dispersal
stochastically ultimate boundedness
extinction