具有时滞和阶段结构的捕食系统的分析

Analysis of a Predator-Prey System with Delay and Stage Structure

建立了一类具有时滞和阶段结构的捕食系统。首先分析了系统的非负不变性、边界平衡点及正平衡点的局部稳定性;其次讨论了边界平衡点的全局渐近稳定性。当时滞τ由0变化到τ0时,系统在平衡点附近发生Hopf分支,即当τ增加通过临界值τ0时。

In this paper, a predator-prey system of two species with stage structure and time delay is considered. The invariance of non-negativity of solution, global stability of the boundary equilibrium is analyzed. The results show that a loss of stability for positive equilibrium when time delay r increases and a Hopf bifurcation can occur. That is, a periodic solution bifurcates from positive equilibrium as r passes through the critical value τ0.