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Permanence and Extinction of a Generalized Gause‐Type Predator‐Prey System with Periodic Coefficients

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  • Jinhuo Luo

Abstract

We study the permanence and extinction of a generalized Gause‐type predator‐prey system with periodic coefficients. We provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent and a sufficient condition for the existence of a periodic solution. In addition we prove that when the predator population tends to extinction, the prey population keeps oscillating above a positive population level.

Suggested Citation

  • Jinhuo Luo, 2010. "Permanence and Extinction of a Generalized Gause‐Type Predator‐Prey System with Periodic Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:845606
    DOI: 10.1155/2010/845606
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    References listed on IDEAS

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    1. Can-Yun Huang & Min Zhao & Hai-Feng Huo, 2008. "Permanence of Periodic Predator‐Prey System with Functional Responses and Stage Structure for Prey," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    2. Can-Yun Huang & Min Zhao & Hai-Feng Huo, 2008. "Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-15, October.
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    Cited by:

    1. Min Zhao & Chuanjun Dai, 2014. "Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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