Computing the Heteroclinic Bifurcation Curves in Predator–prey Systems with Ratio-dependent Functional Response
Computing the Heteroclinic Bifurcation Curves in Predator–prey Systems with Ratio-dependent Functional Response
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通讯作者：
S. Ruan;Yilei Tang;Weinian Zhang;S. Ruan;Y. Tang;W Zhang
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作者：
S. Ruan;Yilei Tang;Weinian Zhang;S. Ruan;Y. Tang;W Zhang
具有Michaelis-Menten-Holling型比率依赖功能反应的捕食者-食饵模型具有非常丰富和复杂的动力学行为，如退化平衡点的存在性、极限环和异宿环的出现以及两个吸引平衡点的共存.本文研究了一类捕食-食饵模型的异宿分支。我们首先通过将模型转化为一个Hamilton系统来计算高阶Melnikov函数，然后给出一个计算高阶近似异宿分歧曲线的算法。123 224 S. Ruan等
Predator–prey models with Michaelis–Menten–Holling type ratio-dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and hetero-clinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator–prey model. We first calculate the higher order Melnikov functions by transforming the model into a Hamiltonian system and then provide an algorithm for computing higher order approximations of the hetero-clinic bifurcation curves. 123 224 S. Ruan et al.