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Graph-theoretic approach to stability of multi-group models with dispersal

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  • This paper is mainly concerned with the issue of stability for multi-group models with dispersal (MGMD). A system on multi-digraph is used to model the MGMD. The popular single graph-based method has been successfully generalized into multi-digraph-based approach. More precisely, by constructing a Lyapunov function for general MGMD, some simple yet less conservative conditions are derived for the stability of MGMD. Furthermore, the graph-theoretic method on multi-graph is successfully applied on predator-prey model with dispersal and coupled oscillators on two digraphs. Subsequently, numerical results are presented to demonstrate the effectiveness of the proposed new technique.
    Mathematics Subject Classification: Primary: 34K20; Secondary: 34C15, 92B99.

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