Stability and Hopf bifurcation analysis on a delayed Leslie-Gower predator-prey system incorporating a prey refuge
Stability and Hopf bifurcation analysis on a delayed Leslie-Gower predator-prey system incorporating a prey refuge
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DOI：
10.1016/j.amc.2012.10.069
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Yongkun Li;Changzhao Li
中科院分区：
文献类型：
--
作者：
Yongkun Li;Changzhao Li
本文研究了一种改进的带有时间延迟的 Leslie-Gower 捕食者-被捕食系统，其中时间延迟被视为分叉参数。通过分析相应的特征方程，考虑正平衡的局部稳定性。此外，我们还表明，当时间延迟超过某些临界值时，就会发生 Hopf 分岔。通过推导描述中心流形上的流动方程，我们给出了确定Hopf分岔方向和分岔周期解稳定性的公式。此外，我们还利用Wu的全局Hopf分岔结果尝试了周期解的全局存在性[J.吴，对称泛函微分方程和带记忆的神经网络，Trans。阿米尔。数学。苏克。 350 (1998) 4799–4838.] 用于函数微分方程。进行数值模拟来说明理论结果，并表明所考虑的系统中的时滞会破坏系统的稳定性。
In this paper, a modified Leslie-Gower predator–prey system with time delays is investigated, where the time delays are regarded as bifurcation parameters. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is considered. Moreover, we show that Hopf bifurcations occur when time delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. In addition, we also try on the global existence of periodic solutions by using the global Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799–4838.] for functional differential equations. Numerical simulations are carried out to illustrate the theoretical results and they show that the time delays in the system under consideration can destroy the stability of the system.