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Global Stability of a Discrete Mutualism Model

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  • Kun Yang
  • Xiangdong Xie
  • Fengde Chen

Abstract

A discrete mutualism model is studied in this paper. By using the linear approximation method, the local stability of the interior equilibrium of the system is investigated. By using the iterative method and the comparison principle of difference equations, sufficient conditions which ensure the global asymptotical stability of the interior equilibrium of the system are obtained. The conditions which ensure the local stability of the positive equilibrium is enough to ensure the global attractivity are proved.

Suggested Citation

  • Kun Yang & Xiangdong Xie & Fengde Chen, 2014. "Global Stability of a Discrete Mutualism Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:709124
    DOI: 10.1155/2014/709124
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    References listed on IDEAS

    as
    1. Tursuneli Niyaz & Ahmadjan Muhammadhaji, 2013. "Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls," International Journal of Differential Equations, Hindawi, vol. 2013, pages 1-9, May.
    2. Yongkun Li, 2005. "Positive periodic solutions of a discrete mutualism model with time delays," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-8, January.
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    Cited by:

    1. Baoguo Chen, 2016. "Permanence for the Discrete Competition Model with Infinite Deviating Arguments," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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