Holling-Tanner型捕食模型的稳定性和Hopf分岔  

Stability and Hopf Bifurcation in the Holling-Tanner Predator-Prey Model

作　　者：孙春杰 SUN Chunjie(School of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《内江师范学院学报》2021年第8期48-52,共5页Journal of Neijiang Normal University

基　　金：国家自然基金项目(615630224)。

摘　　要：考虑了Holling-Tanner型捕食模型,获得了该模型正平衡点的局部渐近稳定性和Hopf分岔的存在性以及Hopf分岔的方向和分岔周期解的稳定性,并利用Matlab软件包进行数值模拟,验证了所获得的理论结果.The Holling-Tanner predator-prey model is considered and the local asymptotic stability of the positive equilibrium point,the existence of Hopf bifurcation,the direction of bifurcation and the stability of bifurcation cycle are obtained.By calculating the first-order Lyapunov quantity,the conditions for the system to generate stable(unstable)limit cycles are given.Numerical simulations are done to verify the obtained theoretical results by use of MATLAB software package.

关 键 词：Holling-Tanner型捕食模型 HOPF分岔 稳定性 周期解 

分 类 号：O175.26[理学—数学]