Existence of a polycycle in non-Lipschitz Gause-type predator–prey models

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• 作者：José ; Luis Bravo ; Manuel Ferná ; ndez ; Manuel Gá ; mez ; Bertha Granados ; Antonio Tineo
• 关键词：Predator– ; prey ; Heteroclinic ; Polycycle
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 January 2011
• 年：2011
• 卷：373
• 期：2
• 页码：512-520
• 全文大小：193 K

文摘

We study Gause-type predator–prey models when the interaction between predator and prey is not locally-Lipschitz continuous in the absence of one of them. We shall show that in this case there appears a polycycle, which affects the existence of limit cycles for the system. We apply the results to study the existence of limit cycles for a classical Gause system.