Stability and bifurcation in a delayed predator–prey system with Beddington–DeAngelis functional response
Stability and bifurcation in a delayed predator–prey system with Beddington–DeAngelis functional response
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DOI：
10.1016/j.jmaa.2004.04.051
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发表时间：
2004-08
影响因子：
1.3
通讯作者：
Zhihua Liu;R. Yuan
中科院分区：
文献类型：
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作者：
Zhihua Liu;R. Yuan
考虑一类具有Beddington-DeAngelis功能反应的时滞捕食-食饵系统.通过分析相关的特征超越方程，研究了内部平衡点的稳定性。通过选取时滞τ作为分支参数，证明了当时滞τ超过某个临界值时，系统会发生Hopf分支.利用Faria和Magalhenes给出的导出规范形的方法，研究了Hopf分支的方向和稳定性。给出了一个例子，并进行了数值模拟来说明所得到的结果。
We consider a delayed predator–prey system with Beddington–DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results.