Hopf bifurcation of a ratio-dependent predator–prey system with time delay

Canan Celik

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Hopf bifurcation of a ratio-dependent predator–prey system with time delay

机译：具有时滞的比率依赖型捕食系统的Hopf分支

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摘要

In this paper, we consider a ratio dependent predator–prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.

机译：在本文中，我们考虑具有比率滞后的比率依赖的捕食者—食饵系统，其中动力学是逻辑的，其承载能力与猎物种群成比例。通过将时延作为分岔参数，基于正则形式方法和中心流形理论，分析了系统的稳定性和Hopf分岔。最后，我们通过数值模拟说明了我们的理论结果。

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《Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science》 |2009年第3期|共11页
作者
Canan Celik;
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正文语种 eng
中图分类动力系统理论;
关键词
bifurcation; predator; system;

机译：分叉;捕食者;系统;

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专利

1. Hopf bifurcations of a ratio-dependent predator-prey model involving two discrete maturation time delays [J] . Esra Karaoglu, Huseyin Merdan Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2014,第Null期

机译：具有两个离散成熟时滞的比率依赖的捕食者-食饵模型的Hopf分叉
2. Hopf Bifurcation Analysis and Stability for a Ratio-Dependent Predator-Prey Diffusive System with Time Delay [J] . International journal of bifurcation and chaos in applied sciences and engineering . 2020,第3期

机译：随着时间延迟的比例依赖性捕食者 - 猎物蔓延系统的HOPF分配分析和稳定性
3. Stability and Hopf bifurcation for a ratio-dependent predator-prey system with stage structure and time delay [J] . Lingshu Wang, Guanghui Feng Advances in Difference Equations . 2015,第1期

机译：具阶段结构和时滞的比率型捕食者-食饵系统的稳定性和Hopf分支。
4. Hopf Bifurcation Analysis and Control of a Ratio-Dependent Predator–Prey Model of Holling IV Type with Time Delayed Feedback [C] . Sun Fengxin, Lin Yiping, Wang Jufeng 2010 Third International Workshop on Chaos-Fractals Theories and Applications . 2010

机译：具有时滞反馈的具有比率的Holling IV型捕食者－食饵模型的Hopf分叉分析和控制
5. Hopf bifurcation control for time-delay dynamical systems and applications. [D] . Chen, Zhen. 2006

机译：时滞动力系统和应用的Hopf分叉控制。
6. Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge [O] . Qingsong Liu, Yiping Lin, Jingnan Cao 2014

机译：带有食饵避难所的两时滞莱斯利-高尔捕食者-食饵系统的全局Hopf分叉
7. Stability and Hopf bifurcation for a ratio-dependent predator-prey system with stage structure and time delay [O] . Lingshu Wang, Guanghui Feng 2015

机译：具阶段结构和时滞的比率型捕食者-食饵系统的稳定性和Hopf分支。

Hopf bifurcation of a ratio-dependent predator–prey system with time delay

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