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On the dynamics of a stochastic ratio-dependent predator–prey model with a specific functional response

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Abstract

In this paper, a new stochastic two-species predator–prey model which is ratio-dependent and a specific functional response is considered in, is proposed. The existence of a global positive solution to the model for any positive initial value is shown. Stochastically ultimate boundedness and uniform continuity are derived. Moreover, under some sufficient conditions, the stochastic permanence and extinction are established for the model. At last, numerical simulations are carried out to support our results.

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Acknowledgments

   The research have been supported by The Natural Science Foundation of China (11261004) and The Natural Science Foundation of Jiangxi Province(20122BAB211010).

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Authors and Affiliations

  1. Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, 341000, People’s Republic of China

    Yan Zhang, Shujing Gao & Yanfei Dai

  2. School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou, 341000, People’s Republic of China

    Kuangang Fan

Authors
  1. Yan Zhang
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  2. Shujing Gao
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  3. Kuangang Fan
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  4. Yanfei Dai
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Correspondence to Yan Zhang.

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Zhang, Y., Gao, S., Fan, K. et al. On the dynamics of a stochastic ratio-dependent predator–prey model with a specific functional response. J. Appl. Math. Comput. 48, 441–460 (2015). https://doi.org/10.1007/s12190-014-0812-3

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  • DOI: https://doi.org/10.1007/s12190-014-0812-3

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