一类具有时滞的Leslie-Gower捕食-食饵模型的Hopf分支

Hopf Bifurcation of a Class of Leslie-GowerPredator-Prey Models with Time Delay

利用Hopf分支理论,研究一类具有时滞的Leslie-Gower捕食-食饵模型.首先,以时滞为分支参数,讨论该模型正平衡点的稳定性和Hopf分支的存在性;其次,根据偏泛函微分方程的规范型理论和中心流形定理,确定Hopf分支的分支方向和分支周期解的稳定性;最后,利用MATLAB进行数值模拟.

Using the Hopf bifurcation theory,we studied a class of Leslie-Gower predator-prey models with time delay.Firstly,taking time delay as the bifurcation parameter,we discussed the stability of the positive equilibrium point of the model and the existence of Hopf bifurcation.Secondly,according to the normal form theory and center manifold theorem for partial differential equation,we derived the direction of Hopf bifurcation and the stability of bifurcation periodic solutions.Finally,we used MATLAB for numerical simulations.