Bifurcation and chaos of a delayed predator-prey model with dormancy of predators
Bifurcation and chaos of a delayed predator-prey model with dormancy of predators
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DOI：
10.1007/s11071-012-0368-4
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发表时间：
2012-03
影响因子：
5.6
通讯作者：
Jingnan Wang;Weihua Jiang
中科院分区：
文献类型：
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作者：
Jingnan Wang;Weihua Jiang
研究了一类捕食者处于休眠状态的时滞捕食-食饵模型。结果表明，食饵种群增长的时滞可以导致在共存平衡点发生具有稳定开关的Hopf分支。给出了Hopf分支周期解的稳定性和方向的计算公式。在适当的条件下，证明了该时滞模型的一致持续生存性。在这个简单的模型中，多个周期解共存。通过数值模拟，表明不同的时滞值可以产生或消除混沌。从生物学的角度来看，我们的结果暗示了该时滞系统的动力学行为强烈依赖于该模型的初始密度和食饵的生长时滞。
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.