Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

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• 作者：N. Ali ; M. Jazar
• 关键词：Predator ; prey model ; Crowley ; Martin functional response ; Permanence ; Limit cycles ; Global stability ; 34D23 ; 92D25
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：43
• 期：1-2
• 页码：271-293
• 全文大小：872KB
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• 作者单位：N. Ali (1)
  M. Jazar (2)
  
  1. Laboratoire de Mathématiques, Image et Applications, Université de La Rochelle, La Rochelle, France
  2. LaMA-Liban, Azm Research Center, Tripoli, Lebanon
  
• ISSN：1865-2085

文摘

In this paper, we study a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses. We show the existence of a bounded positive invariant and attracting set. The possibility of existence and uniqueness of positive equilibrium are considered. The asymptotic behavior of the positive equilibrium and the existence of Hopf-bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered. The existence and non-existence of periodic solutions are established under suitable conditions. The permanence conditions are also established. We obtained sufficient conditions to ensure the global stability of the unique positive equilibrium, by using suitable Lyapunov functions, LaSalle invariance principle and Dulac’s criterion. We obtained also sufficient conditions for the global stability of the prey-extinction equilibrium when the unique positive equilibrium is not feasible. Finally, numerical simulations are presented to illustrate the analytical results.