Turing instability and Hopf bifurcation in a diffusive Leslie–Gower predator–preymodel
Turing instability and Hopf bifurcation in a diffusive Leslie–Gower predator–preymodel
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扩散 Leslie–Gower 捕食者–猎物模型中的图灵不稳定性和 Hopf 分岔
DOI：
10.1002/mma.3853
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Liu Yangyang
中科院分区：
文献类型：
--
作者：
Peng Yahong;Liu Yangyang
本文考虑了一类具有Holling-Ⅱ型和修正的Leslie-Gower功能反应的反应扩散捕食-食饵系统.对于常微分方程，研究了正平衡点的局部稳定性，得到了具体的条件。对于偏微分方程，我们考虑解的耗散性和持久性，平衡解的Turing不稳定性，以及Hopf分支。通过计算规范形，推导出了由系统的初始参数确定Hopf分岔方向和稳定性的公式。我们也使用一些数值模拟来说明我们的理论结果。版权所有© 2016约翰威利父子有限公司.
In this paper, a reaction‐diffusion predator–prey system that incorporates the Holling‐type II and a modified Leslie‐Gower functional responses is considered. For ODE, the local stability of the positive equilibrium is investigated and the specific conditions are obtained. For partial differential equation, we consider the dissipation and persistence of solutions, the Turing instability of the equilibrium solutions, and the Hopf bifurcation. By calculating the normal form, we derive the formulae, which can determine the direction and the stability of Hopf bifurcation according to the original parameters of the system. We also use some numerical simulations to illustrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.