具有Allee效应的加性随机捕食模型的动力学研究

Dynamics Analysis of an Additive Stochastic Predator-Prey Model with Allee Effect

生态系统中捕食者和被捕食者受到群聚生活的影响,Allee效应充分反映种群大小、密度及其增长率之间的相互作用。同时,生态系统会受到随机因素的影响。因此,本文研究具有Allee效应的加性随机捕食模型的动力学行为。通过构造恰当随机Lyapunov函数,得到了种群灭绝的充分条件,以及建立了遍历稳态分布的充分条件。此外,给出相关数值仿真验证的结果。

Predators and prey in ecosystems are affected by social life,and the Allee effect fully reflects the interaction between popu⁃lation size,density,and growth rate.And then,ecosystems are subject to random factors.Therefore,the dynamic behavior of additive stochastic prey-predator model with Allee effect are studied in this paper.By constructing a suitable stochastic Lyapunov function,we obtain sufficient conditions for extinction of the predator species and establish sufficient conditions for the existence of an ergodic sta⁃tionary distribution of the positive solution to such system.In addition,some numerical simulation results are given.