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

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