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Global stability of periodic solutions for a discrete predator–prey system with functional response

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Abstract

The purpose of this paper is to study the existence and global stability of a periodic solution for a discrete predator–prey system with the Beddington–DeAngelis functional response and predator cannibalism. By using the continuation theorem, the existence conditions of at least one periodic solution are obtained, and the sufficient conditions, which ensure the global stability of the positive periodic solution, are derived by constructing a special Lyapunov function.

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Acknowledgements

The research was partially supported by the National Natural Science Foundation of China under Grants (11171314 and 11147015), Natural Science Foundation of Shan’Xi Province Grant No. 2012021002-1, and the Program for Basic Research (2010011007).

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Authors and Affiliations

  1. School of Mechatronic Engineering, North University of China, Taiyuan, 030051, People’s Republic of China

    Li Li & Zhi-Jun Wang

  2. Department of Mathematics, Taiyuan Institute of Technology, Taiyuan, Shan’xi, 030008, People’s Republic of China

    Li Li

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  1. Li Li
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  2. Zhi-Jun Wang
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Correspondence to Li Li.

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Li, L., Wang, ZJ. Global stability of periodic solutions for a discrete predator–prey system with functional response. Nonlinear Dyn 72, 507–516 (2013). https://doi.org/10.1007/s11071-012-0730-6

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  • DOI: https://doi.org/10.1007/s11071-012-0730-6

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