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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