Hybrid control of Hopf bifurcation in a Lotka-Volterra predator-prey model with two delays

Advances in Difference Equations

Zhengdi Zhang¹  Xuedi Wang¹  Miao Peng¹ 

[1] Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, P.R. China

关键词: Hopf bifurcation;    hybrid control;    predator-prey model;    stability;   

DOI  :  10.1186/s13662-017-1434-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the Hopf bifurcation control for a Lotka-Volterra predator-prey model with two delays is studied by using a hybrid control strategy. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation with respect to both delays are established. In addition, the onset of an inherent bifurcation is delayed. Based on the normal form theory and the center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and stability of the bifurcating periodic solution. Numerical simulation results confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

【 授权许可】

CC BY