Bifurcation and chaos of a delayed predator-prey model with dormancy of predators
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- 作者：Jingnan Wang (12) jnwang2006@yahoo.com.cn
Weihua Jiang (1) jiangwh5@yahoo.com.cn - 关键词：Predator ; prey model with dormancy of predators – ; Hopf bifurcation – ; Uniform persistence – ; Time delay – ; Stability
- 刊名：Nonlinear Dynamics
- 出版年：2012
- 出版时间：September 2012
- 年：2012
- 卷：69
- 期：4
- 页码：1541-1558
- 全文大小：1.4 MB
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- 刊物类别：Engineering
- 刊物主题：Vibration, Dynamical Systems and Control
Mechanics
Mechanical Engineering
Automotive and Aerospace Engineering and Traffic - 出版者：Springer Netherlands
- ISSN：1573-269X
文摘
In this paper, a delayed predator-prey model with dormancy of predators is investigated. It shows that time delay in the prey-species growth can lead to the occurrence of Hopf bifurcation with stability switches at a coexistence equilibrium. The computing formulas of stability and direction of the Hopf bifurcating periodic solutions are given. Under appropriate conditions, the uniform persistence of this model with time delay is proved. In this simple model, multiple periodic solutions coexist. Through numerical simulation, it is shown that different values of time delay can generate or eliminate chaos. Biologically, our results imply that dynamical behaviors of this system with time delay strongly depend on the initial density of this model and the time delay of the growth of the prey.