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Analysis of stability for a discrete ratio-dependent predator-prey system

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  • Guangye Chen

    (Xinjiang University)

  • Zhidong Teng

    (Xinjiang University)

  • Zengyun Hu

    (Xinjiang University)

Abstract

The paper investigated the dynamical behaviors of a two-species discrete ratio-dependent predator-prey system. The local stability of the equilibria is obtained by using the linearization method. Further, a new sufficient condition on the global asymptotic stability of the positive equilibrium is established by using an iteration scheme and the comparison principle of difference equations.

Suggested Citation

  • Guangye Chen & Zhidong Teng & Zengyun Hu, 2011. "Analysis of stability for a discrete ratio-dependent predator-prey system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(1), pages 1-26, February.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:1:d:10.1007_s13226-011-0001-0
    DOI: 10.1007/s13226-011-0001-0
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    References listed on IDEAS

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    1. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    3. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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    Cited by:

    1. Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.

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