Multiple bifurcations in a predator-prey system with monotonic functional response
Multiple bifurcations in a predator-prey system with monotonic functional response
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DOI：
10.1016/j.amc.2005.03.010
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Lin-Lin Wang-Lin;Yong-Hong Fan;Wan-Tong Li
中科院分区：
文献类型：
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作者：
Lin-Lin Wang-Lin;Yong-Hong Fan;Wan-Tong Li
本文研究了一类具有Holling Ⅲ型功能性反应的捕食者-食饵系统的动力学，当h=0时，Chen和Zhang（J. P. Chen，H.D. Zhang，具有Holling Ⅲ型功能性反应的两种群捕食者-食饵模型的定性分析，Appl.Math.Mech.7（1）（1986）73-80）和Kazarinoff和Driessche（N.D.张文，货车，一个具有功能反应的捕食-被捕食系统，生物科学学报。39（1-2）（1978）125-134）对上述系统进行了定性分析，得到了正平衡点和极限环存在和稳定的一些条件。他们得出的动力学现象是正常的，不存在退化奇点。但是当存在不断收获时，我们将证明系统可能具有更复杂和更丰富的动力学。通过选取捕食者的死亡率和收获率作为分支参数，对系统进行了分支分析，证明了系统可以发生Bogdanov-Takens分支。并给出了所有简并结构的图形。
In this paper, we study the dynamics of a predator–prey system with Holling type III functional response of the formWhen h=0, Chen and Zhang (J.P. Chen, H.D. Zhang, The qualitative analysis of two species predator–prey model with Holling’s type III functional response, Appl. Math. Mech. 7 (1) (1986) 73–80) and Kazarinoff and Driessche (N.D. Kazarinoff, P. Van Den Driessche, A model predator–prey system with functional response, Math. Biosci. 39 (1–2) (1978) 125–134) gave qualitative analysis of the above system and obtained some conditions for the existence and stability of positive equilibria and limit cycles. The dynamical phenomena they concluded are normal, and there is no degenerate singularities. But when the constant harvesting is present, we will show that the system may have more complex and more rich dynamics. We carry out bifurcation analysis by choosing the death rate and the harvesting rate of the predator as the bifurcation parameters and show that the system can undergo the Bogdanov–Takens bifurcation. Also the figures of all degenerate structures are given.