College of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021, China.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China.
Chaos. 2019 Jan;29(1):013101. doi: 10.1063/1.5078814.
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation and double Hopf bifurcation are investigated on the parametric plane of two delays. Taking two time delays as bifurcation parameters, the normal form on the center manifold near the double Hopf bifurcation point is derived, and the unfoldings near the critical points are given. Finally, we obtain the complex dynamics near the double Hopf bifurcation point, including the existence of quasi-periodic solutions on a 2-torus, quasi-periodic solutions on a 3-torus, and strange attractors.
本文研究了具有两个时滞和扩散的修正 Leslie-Gower 捕食者-被捕食系统的动力学。通过计算稳定性切换曲线，在两个时滞的参数平面上研究了正平衡点的稳定性和 Hopf 分支与双 Hopf 分支的存在性。以两个时滞作为分岔参数，在双 Hopf 分岔点附近的中心流形上导出正规形，并给出临界点附近的展开。最后，我们得到了双 Hopf 分岔点附近的复杂动力学，包括在 2-环面上存在拟周期解、在 3-环面上存在拟周期解和奇异吸引子。
