Lyapunov direct method for investigating stability of nonstandard finite difference schemes for metapopulation models |
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Authors: | Quang A Dang Manh Tuan Hoang |
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Institution: | 1. Center for Informatics and Computing, Vietnam Academy of Science and Technology (VAST), Hanoi, Vietnam.;2. Institute of Information Technology, Vietnam Academy of Science and Technology (VAST), Hanoi, Vietnam. |
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Abstract: | In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of the Lyapunov stability theorem. As a result of this we have proved that the NSFD schemes preserve essential properties of the metapopulation models (positivity, boundedness and monotone convergence of the solutions, equilibria and their stability properties). Especially, the basic reproduction number of the continuous models is also preserved. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes. The method of Lyapunov functions proves to be much simpler than the standard method for studying stability of the discrete metapopulation model in our very recent paper. |
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Keywords: | Metapopulation model nonstandard finite-difference scheme dynamically consistent Lyapunov stability theory global stability |
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