具有时滞的Logistic模型的分支问题的频域分析

研究一类具有时滞的Logistic模型。运用频域法并分析该模型对应的特征方程,得到了系统Hopf分支点,通过选择时滞τ作为参数,发现当参数通过某一临界值时,Hopf分支产生,Hopf分支产生,同时得到了系统正平衡点稳定的时滞范围处于零与某个正常数之间,数值模拟验证当时滞τ=τ0时,系统的正平衡点是局部稳定的,当τ>τ0时,系统的正平衡点是不稳定的。

Frequency Domain Analysis for Bifurcation in a Logistic Model with Delay

In this paper,a class of logistic model with delay is considered.By applying the frequency domain approach and analyzing the associated characteristic equation,the existence of bifurcation parameter point is determined.If the coefficient τ is chosen as a bifurcation parameter,it is found that Hopf bifurcation occurs when the parameter τ passes through a critical value τk.The length of delay which preserves the stability of the positive equilibrium is calculated to be between zero and a certain positive constant τ+.Some numerical simulations show that when the delay τ passes through the critical value τ0,the positive equilibrium is locally stable and unstable when the delay τ>τ0.