一类具有时滞的生态模型的Hopf分支

Hopf bifurcation for a class ecological model of delays

研究了一类具有连续时滞与离散时滞的单种群模型的无条件稳定与Hopf分支问题.首先利用特征值理论得到了模型无条件稳定的充要条件,从而说明时滞为无害时滞,再以时滞τ为参数,给出了Hopf分支的存在性条件及分支值处模型平衡态的稳定性.

Absolute stability and Hopf bifurcation for a class ecological model with the distributed and distete delay are investigated. Sufficient conditions of absolute stabiltiy are obtained by using the theory of characteristic value, and it is shown that the delay r is locally harmless. Furthermore, regarding the delay as a parameter, conditions of the existence of Hopf bifurcation and the stability of model at τ0 are given.