具反馈控制单种群时滞模型的Hopf分支的频域分析

Frequency Domain Analysis for Bifurcation of a Logistic Growth Model with Feedback Control and Delay

研究了一类具反馈控制单种群时滞模型.选择时滞τ为分支参数,得到了:当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解.最后,用数值模拟验证了分析结果的正确性.

In this paper,a logistic growth feedback control model with single species delay is investigated.By choosing the delay τ as a bifurcation parameter,we show that Hopf bifurcation can occur when τ passes a sequence of critical values,which means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter τ exceeds a critical value.Some numerical simulations are given to verify the validity of the theoretical analysis results.