Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response
Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response
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DOI：
10.1006/jdeq.2000.3982
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发表时间：
2001-11
影响因子：
2.4
通讯作者：
Dongmei Xiao;S. Ruan
中科院分区：
文献类型：
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作者：
Dongmei Xiao;S. Ruan
摘要利用Faria和Magalhaes发展的时滞泛函微分方程的范式理论，研究了一类具有非单调功能反应的时滞捕食者-食饵系统。对模型的分叉分析表明，对于任意时滞值，模型都存在Bogdanov-Takens奇点。得到了该模型在Bogdanov-Takens奇点的横向展开。另一方面，对于某些参数，小时滞改变了模型平衡点的稳定性，当时滞超过某一临界值时，系统会出现Hopf分叉。
Abstract A delayed predator–prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhaes. The bifurcation analysis of the model indicates that there is a Bogdanov–Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov–Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.