一类害虫-天敌生态模型的Hopf分支分析

Hopf bifurcation analysis on a class of delayed natural pest-enemy system

对一类时滞害虫-天敌生态模型进行了分析,通过分析其相应线性近似系统的特征方程,讨论了平衡点的局部稳定性.同时选取时滞τ为分支参数,得到了模型在正平衡点处当参数在临界值附近变化时系统会产生Hopf分支的充分条件.最后给出一个具体的例子来说明理论结果的正确性.

A class of natural pest-enemy system with time delays is considered,where the time delay is regarded as bifurcation parameter.By analyzing the corresponding characteristic equation,the local stability of equilibriums is investigated.Moreover,we show that Hopf bifurcations occurs when time delay crosses some critical values.A numerical simulation is carried out to illustrate the theoretical results.