具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower项与Holling-III类功能性反应函数的时滞捕食系统. 以时滞为分支参数, 讨论系统正平衡点的局部稳定性, 给出系统产生Hopf分支的时滞关键值. 进一步, 确定系统Hopf分支的方向与分支周期解稳定性, 并对系统全局分支周期解的存在性进行讨论. 最后, 利用仿真实例验证理论分析结果的正确性.

Hopf Bifurcation in a Delayed Predator-prey System with Modified Leslie-Gower and Holling-type III Schemes

In this paper, we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes. By regarding the time delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. And we find that Hopf bifurcations can occur as the time delay crosses some critical values. In particular, special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. In addition, the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result. Finally, numerical simulations are carried out to illustrate the main theoretical results.