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Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays

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  • Nai-Wei Liu
  • Ting-Ting Kong

Abstract

We consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov function, we prove that the positive equilibrium is locally asymptotically stable under a sufficient condition. Finally, by using comparison theorem and the -limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the global asymptotic stability.

Suggested Citation

  • Nai-Wei Liu & Ting-Ting Kong, 2014. "Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, May.
    • Handle: RePEc:hin:jnlaaa:930762
    DOI: 10.1155/2014/930762
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