Lyapunov direct method for investigating stability of nonstandard finite\n difference schemes for metapopulation models

2017/01/19 by Đặng Quang Á, Dang, Quang A, Manh Tuan Hoang +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Applied mathematics #Computer science #Finite difference #Gene Regulatory Network Analysis #Generalization #Lyapunov function #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Metapopulation #Nonlinear system #Physics #Stability (learning theory)

paper · pdf · doi:10.48550/arxiv.1701.05667

openalex publication_date 2017/01/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper nonstandard finite difference (NSFD) schemes of two\nmetapopulation models are constructed. The stability properties of the discrete\nmodels are investigated by the use of a generalization of Lyapunov stability\ntheorem. Due to this result we have proved that the NSFD schemes preserve all\nproperties of the metapopulation models. Numerical examples confirm the\nobtained theoretical results of the properties of the constructed difference\nschemes. The method of Lyapunov functions proves to be much simpler than the\nstandard method for studying stability of the discrete metapopulation model in\nour very recent paper.\n

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