| Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-Ⅳ Functional Response |
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| 作者姓名： | Ji-caiHuang Dong-meiXiao |
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| 作者单位： | Ji-cai Huang~1 Dong-mei Xiao~2
1 Academy of Mathematics and Systems Science，Academia Sinica，Beijing 100080，China
2 Department of Mathematics，Shanghai Jiao Tong University，Shanghai 200030，China |
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| 基金项目： | Supported by Chinese Academy of Sciences (KZCX2-SW-118)，Supported by the NNSF of China (No.10071027，No.10231020) |
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| 摘 要： | In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳfunctionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.
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| 关 键 词： | 分歧理论 稳定性 功能响应 数字模拟 极限环 人口动态 |
| 收稿时间： | 23 May 2003 |
Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-IV Functional Response |
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| Ji-caiHuang Dong-meiXiao.Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-IV Functional Response[J].Acta Mathematicae Applicatae Sinica,2004,20(1):167-178. |
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| Authors: | Email author" target="_blank">Ji-cai?HuangEmail author Dong-mei?Xiao |
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| Institution: | (1) Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100080, China;(2) Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China |
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| Abstract: | Abstract
In this paper the dynamical behaviors of a predator-prey
system with Holling Type-IV functional response are investigated
in detail by using the analyses of qualitative method,
bifurcation theory, and numerical simulation. The qualitative
analyses and numerical simulation for the model indicate that it
has a unique stable limit cycle. The bifurcation analyses of the
system exhibit static and dynamical bifurcations including
saddlenode bifurcation, Hopf bifurcation, homoclinic bifurcation
and bifurcation of cusp-type with codimension two (ie, the
Bogdanov-Takens bifurcation), and we show the existence of
codimension three degenerated equilibrium and the existence of
homoclinic orbit by using numerical simulation.
1 Supported by Chinese Academy of Sciences
(KZCX2-SW-118);
2 Supported by the NNSF of China (No. 10071027; No.
10231020). |
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| Keywords: | Predator-prey system Limit cycle Bogdanov-Takens bifurcation |
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