Hopf bifurcation analysis and control of a ratio-dependent predator–prey model of Holling Ⅳ type with time delayed feedback

摘要：

In present paper, the time-delayed feedback is coupled with a ratio-dependent predator-prey model of Holling □ type. This predator-prey system can be seen as a human-controlled biological system. Regarding the delay as parameter, we investigate the existence of local Hopf bifurcations. By using the Hassard method and the center manifold argument, we derive the explicit formulas determining the stability, direction and other properties of bifurcation. Finally, we give a numerical simulation, which indicates that when the delay passes through certain critical values, the positive equilibria is converted into a stable steady state. It means that we can control the stability of the equilibria by man-made control of the number of the predator with certain age.

作者: Fengxin Sun Jufeng Wang Yiping lin

作者单位: Ningbo University of Technology Ningbo, China Ningbo Institute of Technology, Zhejiang University Ningbo, China Kunming University of Science and Technology Kunming,China

会议类型: 国际会议

会议名称: 2010国际混沌、分形理论与应用研讨会(IWCFTA 2010)

会议地点: 昆明

会议语种:英文

页码: 72-76

在线出版日期: 2010-10-29（万方平台首次上网日期，不代表论文的发表时间）