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Periodicity in a ratio-dependent predator-prey system with stage structure for predator

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  • Fengde Chen

Abstract

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system with stage structure for predator. The approach involves some new technique of priori estimate. For the system without delay, by constructing a suitable Lyapunov function, some sufficient conditions which guarantee the existence of a unique global attractive positive periodic solution are obtained. Those results have further applications in population dynamics.

Suggested Citation

  • Fengde Chen, 2005. "Periodicity in a ratio-dependent predator-prey system with stage structure for predator," Journal of Applied Mathematics, Hindawi, vol. 2005, pages 1-17, January.
    • Handle: RePEc:hin:jnljam:638384
    DOI: 10.1155/JAM.2005.153
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    Cited by:

    1. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
    2. Chen, Yuanyuan & Changming, Song, 2008. "Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1104-1114.

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