Existence of limit cycles and homoclinic bifurcation in a plant–herbivore model with toxin-determined functional response
Existence of limit cycles and homoclinic bifurcation in a plant–herbivore model with toxin-determined functional response
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具有毒素决定功能反应的植物-草食动物模型中极限环和同宿分岔的存在
DOI：
10.1016/j.jde.2014.12.029
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发表时间：
2015-04
影响因子：
2.4
通讯作者：
Xiuli Cen
中科院分区：
文献类型：
--
作者：
Yulin Zhao;Zhilan Feng;Yiqiang Zheng;Xiuli Cen
In this paper we study a two-dimensional toxin-determined functional response model (TDFRM). The toxin-determined functional response explicitly takes into consideration the reduction in the consumption of plants by herbivore due to chemical defense, which generates more complex dynamics of the plant–herbivore interactions. The purpose of the present paper is to analyze the existence of limit cycles and bifurcations of the model. By applying the theories of rotated vector fields and the extended planar termination principle, we establish the conditions for the existence of limit cycles and homoclinic loop. It is shown that a limit cycle is generated in a supercritical Hopf bifurcation and terminated in a homoclinic bifurcation, as the parameters vary. Analytic proofs are provided for all results, which generalize the results presented in [11].
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DOI：
10.1007/978-0-387-49319-0
发表时间：
1941
期刊：
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影响因子：
--
作者：
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通讯作者：
J. Jost
影响因子：
2.4
作者：
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通讯作者：
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1990
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影响因子：
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通讯作者：
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DOI：
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发表时间：
2012
期刊：
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影响因子：
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作者：
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通讯作者：
K. Soetaert;J. Cash;F. Mazzia
DOI：
10.1016/s0016-0032(61)91021-3
发表时间：
1960
期刊：
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影响因子：
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作者：
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通讯作者：
V. V. Nemytskii-V.