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

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...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2019-08, Vol.18 (2), p.461-475
Main Authors: Dang, Quang A, Hoang, Manh Tuan
Format: Article
Language:English
Subjects:
Computer simulation
Difference and Functional Equations
Dynamic stability
Dynamical Systems and Ergodic Theory
Finite difference method
Liapunov direct method
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-018-0295-y