一类捕食模型的定性分析

Qualitative Analysis of a Predator-Prey Model

建立了一类具有性别结构的捕食模型,应用特征子空间分解与线性化方法得到了常微分方程组正平衡点局部稳定性的充分条件,进一步利用构造适当的Lyapunov泛函的方法得到了正平衡点全局稳定的充分条件,最后给出了模型在一定条件下的数值模拟,也使结论得以验证。

A predator--prey model with sex--structure is formulated. The sufficient condition of local as- ymptotic stability of the positive equilibrium is obtained by using the characteristic decomposition and lin- earization method. Moreover, the global asymptotic stability of the positive equilibrium is established by using and constructing a suitable Lyapunov function. Also, the numerical simulation is given verifying the result of this paper is correct.