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Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models

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Abstract

In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties of the metapopulation model such as positivity, boundedness and monotone convergence of the solutions, equilibria and their stability. The numerical simulations confirm the validity of the obtained theoretical results and the advantages of NSFD schemes over standard finite difference schemes.

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Acknowledgements

This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 102.01-2017.306.

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Authors and Affiliations

  1. Center for Informatics and Computing, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Quang A Dang

  2. Institute of Information Technology, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Manh Tuan Hoang

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  1. Quang A Dang
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  2. Manh Tuan Hoang
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Correspondence to Manh Tuan Hoang.

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Dang, Q.A., Hoang, M.T. Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models. Qual. Theory Dyn. Syst. 18, 461–475 (2019). https://doi.org/10.1007/s12346-018-0295-y

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  • DOI: https://doi.org/10.1007/s12346-018-0295-y

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