具有收获和阶段结构的时滞捕食-食饵模型的Hopf分支

Hopf Bifurcation of Time-delayed Predator-prey Model with Stage Structure and Harvesting

应用微分方程分支理论,研究具有收获和阶段结构的时滞捕食-食饵模型,以时滞τ为分支参数,运用Hopf分支理论进行研究发现,在一定条件下,当时滞τ<τ_0时,正平衡点是局部渐近稳定的,当时滞τ>τ_0时,正平衡点是不稳定的,即当τ经过临界值τ0时系统出现Hopf分支。最后,用Matlab软件进行数值仿真验证了结论的正确性。

Time-delayed predator-prey model with stage structure and harvesting is studied by using the bifurcation method of differential equations. By means of the Hopf bifurcation theorem and considering the delay τ as a bifurcation parameter,the endemic equilibrium is locally stable when τ τ0,and unstable when τ τ0,Hopf bifurcation occurs when τ passes through the critical values τ0. Finally,Matlab is employed to carry out numerical simulation to verify the results.