一类捕食干扰下食饵竞争–定殖模型的进化奇异策略分析

Analysis of Evolutionary Singular Strategies in a Class of Prey Competition-Colonization Model with Predation Interference

摘要: 基于班块化栖息地竞争–定殖特性，本文建立了一类捕食干扰下食饵种群竞争–定殖模型，其中捕食项使用Holling-III型功能反应函数刻画。通过理论分析，我们证明了控制定殖率和捕食率的变化，系统出现尖分岔。特别地，中等程度的定殖率和高强度的捕食率，诱导系统出现双稳态现象。同时，考虑捕食和定殖存在权衡时，我们研究了食饵种群定殖率的长期进化动力学行为。借助临界函数分析方法，我们得到了进化奇异策略稳定性对应的权衡函数的几何性质。

Abstract: Based on the competition-colonization in spatially structured habitats, we consider a class of prey competition-colonization model under predation interference, in which the predation term is characterized by Holling-III functional response functions. Theoretical analysis show that the system exhibits the cusp bifurcation by colonization rate and predation rate. Specifically, moderate colonization rates and high-intensity predation rates induce the bistable phenomenon in the system. Furthermore, considering the trade-off between predation and colonization, we investigate the long-term evolutionary dynamics of the colonization rate. By the method of critical function analysis, we obtain the geometric properties of the trade-off functions corresponding to the stability of evolutionary singular strategies.