具有阶段结构种群模型的局部稳定性分析

Local Stability Analysis of Population Model with Stage Structure

提出了具有阶段结构的食饵——捕食者系统,在该系统中只有食饵具有阶段结构,而且只有成年食饵能够被捕食者捕获,除此之外,该微分代数模型系统以捕食者为捕获努力。微分代数模型系统建立后,利用微分代数系统和分岔理论,研究了模型系统的局部稳定性。结果表明,该微分模型系统在正平衡点附近出现奇异诱导分岔,即系统在正平衡点附近失去稳定性。

In this paper, a predator-prey system with stage-structure is proposed, in which only the prey has stage structure, and only the adult prey can be captured by the predator. In addition, the differential algebraic model system takes the predator as the capture effort. After the differential algebraic model system is established, the local stability of the model system is studied by using the differential algebraic system and bifurcation theory. The results show that the differential model system exhibits singular induced bifurcation near the positive equilibrium point, that is, the system loses stability near the positive equilibrium point.