具有阶段结构的捕食-食饵模型的定性分析

Qualitative analysis on a predator-prey model with stage structure

研究了一类捕食者具有阶段结构的捕食-食饵模型.运用抛物型方程组的比较原理得到了整体解的存在性和半平凡解的全局稳定性.针对稳态问题,给出正解的先验估计及非常数正解的不存在性,同时利用分歧理论研究了一维空间下在3个常数平衡态处的局部分歧、局部分歧解的近似结构以及非常数正解的存在性.

A predator-prey model with stage structure is discussed. Based on the comparison principle for parabolic equations, the global existence of solutions and the global asymptotical stability of a semitrival solution are obtained. For the corresponding steady-state problem, a prior estimate of positive solution and a nonexistence result for non-constant positive solution are given. By using the bifurcation theorem, it is proved that the local bifurcation occurs at the three constant solutions in one dimension case, and the structure of solutions near the bifurcation point and the existence of non-constant positive solutions are discussed.