斑块环境下捕食-食饵系统的全局渐近稳定性

考虑了两斑块环境下带有食饵阶段结构和比例依赖的常系数捕食-食饵系统的动力学行为.首先假设食饵被分为幼年和成年阶段并被限制在每一斑块中而不能进行斑块间的扩散;然后假设幼年食饵没有生育繁殖的能力且没有被猎物捕获的危险.对于捕食者,假设它们可以在斑块间扩散.基于这些假设,通过构造Lyapunov函数得到了该系统正平衡点的全局渐近稳定性的充分条件.

Global Asymptotic Stability of Predator-prey System in Patchy Environment

The dynamic behavior of predator-prey system with constant coefficients and with stage structure of prey and ratio dependence in two-patch environments is considered.First,it is assumed that the prey species is divided into immature and mature stage and that the preys are confined to each of the patches but can not disperse between patches;then it is always supposed that the immature preys do not have the ability to reproduce and can not be captured by predators.For predators,it is supposed that they can disperse between two patches.Under these hypotheses,by constructing Lyapunov functions,the sufficient conditions are obtained for the global asymptotic stability of a positive equilibrium of this system.