Bifurcation analysis of modified Leslie–Gower predator–prey model with Michaelis–Menten type prey harvesting
Bifurcation analysis of modified Leslie–Gower predator–prey model with Michaelis–Menten type prey harvesting
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DOI：
10.1016/j.jmaa.2012.08.057
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发表时间：
2013-02
影响因子：
1.3
通讯作者：
R. Gupta;P. Chandra
中科院分区：
文献类型：
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作者：
R. Gupta;P. Chandra
本文讨论了一类食饵具有非线性收获的修正Leslie-Gower食饵-捕食模型的分支分析。我们给出了一个详细的数学分析模型来描述一些重要的结果，可能会出现从生物资源的相互作用。该模型显示了一个复杂的动态在捕食者-食饵平面。讨论了该模型的持久性、稳定性和分歧（鞍结分歧、跨临界分歧、Hopf-Andronov分歧和Bogdanov-Takens分歧）。从生态学的角度分析了食饵捕获和捕食者增长率对模型的影响，并将它们作为重要的分歧参数.给出了通过Hopf分支出现的极限环的局部存在性和稳定性。通过数值模拟，证明了当Hopf分岔产生的极限环与鞍点碰撞时，同宿环的出现。这项工作反映了物种共存的收获率的可行上界是可以保证的。利用MATLAB进行了数值模拟，以证明所获得的结果。
In the present paper we discuss bifurcation analysis of a modified Leslie–Gower prey–predator model in the presence of nonlinear harvesting in prey. We give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources. The model displays a complex dynamics in the prey–predator plane. The permanence, stability and bifurcation (saddle–node bifurcation, transcritical, Hopf–Andronov and Bogdanov–Takens) of this model are discussed. We have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view. The local existence and stability of the limit cycle emerging through Hopf bifurcation is given. The emergence of homoclinic loops has been shown through simulation when the limit cycle arising though Hopf bifurcation collides with a saddle point. This work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed. Numerical simulations using MATLAB are carried out to demonstrate the results obtained.