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Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge

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Abstract

In this paper, a fractional-order predator-prey model incorporating a prey refuge is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of the solutions for the considered model. Moreover, we also analyze the existence of various equilibrium points, and some sufficient conditions are derived to ensure the global asymptotic stability of the predator-extinction equilibrium point and coexistence equilibrium point. Finally, some numerical simulations are carried out for illustrating the analytic results.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant Nos. 11371287, 11361059, 11271312, 61563048), the International Science and Technology Cooperation Program of China (Grant No. 2010DFA14700), and the Development Project of Innovative Talents of Technological Youth of Xinjiang (Grant No. 2014721014).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Hong-Li Li, Long Zhang, Cheng Hu, Yao-Lin Jiang & Zhidong Teng

  2. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yao-Lin Jiang

Authors
  1. Hong-Li Li
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  2. Long Zhang
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  3. Cheng Hu
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  4. Yao-Lin Jiang
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  5. Zhidong Teng
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Correspondence to Hong-Li Li.

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Li, HL., Zhang, L., Hu, C. et al. Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge. J. Appl. Math. Comput. 54, 435–449 (2017). https://doi.org/10.1007/s12190-016-1017-8

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  • DOI: https://doi.org/10.1007/s12190-016-1017-8

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