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Periodic solution and persistence for a three-species ratio-dependent predator-prey model with time delays in two-patch environments*

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Abstract

The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.

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Authors and Affiliations

  1. College of Sciences, Hubei University of Technology, Wuhan, 430068, China

    Desheng TIAN

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  1. Desheng TIAN
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Correspondence to Desheng TIAN.

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The research is supported by the Scientific Research Foundation of the Doctor Department of Hubei University of Technology.

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TIAN, D. Periodic solution and persistence for a three-species ratio-dependent predator-prey model with time delays in two-patch environments*. J Syst Sci Complex 21, 226–238 (2008). https://doi.org/10.1007/s11424-008-9106-x

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  • DOI: https://doi.org/10.1007/s11424-008-9106-x

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