Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

XiaLiu; YepengXing

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Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

机译：具有避难所和恒定收获的比率相关的Holling-Tanner系统的分叉

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The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.

机译：研究了具有避难和持续收获的捕食系统的分叉性质。平衡数和系统性质将因避难和收获而改变，从而导致发生多种分叉现象，例如，鞍节点分叉，Bogdanov-Takens分叉，Hopf分叉，向后分叉，连接鞍节点和鞍分叉以及异斜叉分叉的等分。与没有庇护和收获的系统相比，我们的主要结果表明该系统具有更丰富的动力。

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《Abstract and applied analysis》 |2013年第14期|共10页
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XiaLiu; YepengXing;
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1. Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting [J] . Xiao DM, Jennings LS SIAM Journal on Applied Mathematics . 2005,第3期

机译：具有恒定比率收获的比率依赖型捕食者－食饵系统的分支
2. Bifurcations and spatiotemporal patterns in a ratio-dependent diffusive Holling-Tanner system with time delay [J] . An Qi, Jiang Weihua Mathematical Methods in the Applied Sciences . 2019,第2期

机译：具有时间延迟的比例依赖扩散HOLLING-TANNER系统中的分叉和时空图案
3. Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System [J] . WenjieZuo Abstract and applied analysis . 2013,第6期

机译：比率依赖的Holling-Tanner扩散系统的全局稳定性和分支
4. Bifurcations of a Ratio-dependent Prodator-prey System with Constant Rate Harvesting [C] . Shanghai international symposium on nonlinear science amp; application . 2003

机译：具有比率的具有比率的捕食者－食饵系统的分支
5. Bifurcation subsystem method and its application to diagnosis of power system bifurcations produced by discontinuities. [D] . Ben-Kilani, Khadija. 1997

机译：分叉子系统方法及其在不连续电力系统分叉诊断中的应用。
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 Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response [O] . Juan Liu, Zizhen Zhang, Ming Fu 2012

机译：延迟HOLLING-TANNER捕食者 - 猎物系统中稳定性和分叉具有比率依赖功能反应

Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

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