Existence of limit cycles in a three level trophic chain with Lotka-Volterra and Holling type II functional responses

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• 作者：Ví ; ctor Castellanos ; ^{vicas@ujat.mx} ; Ramó ; n E. Chan-Ló ; pez ^{eduardo.clopez13@gmail.com}
• 关键词：Food chain ; Leslie&ndash ; Gower scheme ; Stability ; Andronov&ndash ; Hopf bifurcation ; First Lyapunov coefficient
• 刊名：Chaos, Solitons & Fractals
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：95
• 期：Complete
• 页码：157-167
• 全文大小：1329 K
• 卷排序：95

文摘

In this paper we analyze a three level trophic chain model, considering a logistic growth for the lowest trophic level, a Lotka–Volterra and Holling type II functional responses for predators in the middle and in the cusp in the chain, respectively. The differential system is based on the Leslie–Gower scheme. We establish conditions on the parameters that guarantee the coexistence of populations in the habitat. We find that an Andronov–Hopf bifurcation takes place. The first Lyapunov coefficient is computed explicitly and we show the existence of a stable limit cycle. Numerically, we observe a strange attractor and there exist evidence of the model to exhibit chaotic dynamics.