Stability and bifurcation in a stage-structured predator-prey system with Holling-Ⅱ functional response and multiple delays

Zizhen Zhang; Huizhong Yang

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Stability and bifurcation in a stage-structured predator-prey system with Holling-Ⅱ functional response and multiple delays

机译：具有HollingⅡ类功能反应和多重时滞的阶段结构捕食者-食饵系统的稳定性和分岔。

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In this paper, we analyse a delayed Holling-Ⅱ predator-prey system with stage-structure for the prey. At first, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analysing the distribution of the roots of the associated characteristic equation. Then, the explicit formula that determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions from the Hopf bifurcation are established by using the normal form method and centre manifold argument. Finally, some numerical simulations are carried out to support the main theoretical results.

机译：本文分析了具有阶段结构的时滞Holling-Ⅱ捕食者—食饵系统。首先，我们通过分析相关特征方程的根的分布，研究了在正平衡时两个时滞的Hopf分支的稳定性和周期解的存在性。然后，使用范式方法和中心流形参数，建立确定Hopf分支方向和由Hopf分支决定分支周期解的稳定性的显式公式。最后，进行了一些数值模拟以支持主要的理论结果。

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《International journal of computer mathematics》 |2015年第4期|542-561|共20页
作者
Zizhen Zhang; Huizhong Yang;
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作者单位

Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China,School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China;

Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China;

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正文语种 eng
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关键词
predator-prey system; delays; stability; Hopf-bifurcation; stage-structure; periodic solutions;

机译：捕食者－被捕者系统;延误稳定性;Hopf分支阶段结构周期解;

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1. Multiple bifurcations in a delayed predator-prey diffusion system with a functional response [J] . Zhang J.-F., Li W.-T., Yan X.-P. Nonlinear analysis. Real world applications . 2010,第4期

机译：具功能反应的时滞捕食者-食饵扩散系统的多个分叉。
2. Multiple Bifurcations in a Delayed Predator-Prey System with Nonmonotonic Functional Response [J] . Dongmei Xiao, Shigui Ruan Journal of Differential Equations . 2001,第2期

机译：具有非单调功能性反应的时滞捕食-被捕食系统的多个分支
3. Multiple periodic solutions of a delayed stage-structured predator-prey model with non-monotone functional responses [J] . Yonghui Xia, Jinde Cao, Sui Sun Cheng Applied Mathematical Modelling . 2007,第9期

机译：具有非单调功能响应的时滞结构的捕食者－食饵模型的多个周期解
4. Stability and Hopf bifurcation in a delayed predator-prey system with Monod-Haldane functional response and diffusion [C] . Xinyou Meng, Haifeng Huo International congress on mathematical biology;ICMB2011 . 2011

机译：具有Monod-Haldane功能反应和扩散的时滞捕食者-食饵系统的稳定性和Hopf分叉
5. Stability and bifurcation in systems of tri-neurons with multiple time delays. [D] . Li, Lei. 2006

机译：具有多个时滞的三神经元系统的稳定性和分叉性。
6. Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays [O] . Zi-Gen Song, Jian Xu 2013

机译：具有多个延迟的双神经网络系统中的稳定性开关和双Hopf分叉
7. Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response [O] . Jiao Jiang, Yongli Song 2013

机译：具有非单调功能反应的延迟Leslie-Gower捕食者 - 捕食者系统的稳定性和分岔分析

Stability and bifurcation in a stage-structured predator-prey system with Holling-Ⅱ functional response and multiple delays

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