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

Chunmei Zhang; Wenxue Li; Ke Wang

doi:10.3934/dcdsb.2015.20.259

Article Contents

2015, Volume 20, Issue 1: 259-280. Doi: 10.3934/dcdsb.2015.20.259

This issue Previous Article On conformal measures of parabolic meromorphic functions Next Article Functional solution about stochastic differential equation driven by $G$-Brownian motion

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

1.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209

Received: January 31, 2014

Revised: July 31, 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K20; Secondary: 34C15, 92B99.

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