具时滞和Leslie-Gower功能反应函数的捕食者-食饵系统的Hopf分支分析

Analysis of Hopf bifurcation on the Leslie-Gower predator-prey system with time delay

研究了一类带有时滞和Leslie-Gower功能反应函数的捕食者-食饵系统的Hopf分支。给出系统非负平衡点的存在性和稳定性。以时滞作为分支参数,证明了系统在正平衡点附近经历Hopf分支的存在性。利用Matlab对系统进行数值模拟来验证所给出的结论。

Hopf bifurcation of the Leslie-Gower predator-prey system with time delay is analyzed in this paper.The existence and stability of the nonnegative equilibria are discussed.Using the time delay as the bifurcating value,we investigate that the system undergoes Hopf bifurcation near the positive equilibrium under some conditions.Numerical simulation is given to illustrate our conclusions via Matlab software.