Stability analysis for discrete-time coupled systems with multi-diffusion by graph-theoretic approach and its application

Huan  Su; Pengfei  Wang; Xiaohua  Ding

doi:10.3934/dcdsb.2016.21.253

Article Contents

2016, Volume 21, Issue 1: 253-269. Doi: 10.3934/dcdsb.2016.21.253

This issue Previous Article Long-time behavior of solutions of the generalized Korteweg--de Vries equation Next Article An almost periodic epidemic model in a patchy environment

Stability analysis for discrete-time coupled systems with multi-diffusion by graph-theoretic approach and its application

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

Received: December 31, 2014

Revised: June 30, 2015

Published: December 2015

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Abstract

In this paper, we investigate the global stability of discrete-time coupled systems with multi-diffusion (DCSMDs). By utilizing a multi-digraph theory, we construct a global Lyapunov function for DCSMDs. Consequently, some sufficient conditions are presented to ensure the stability of a general DCSMDs. Then the proposed theory is successfully applied to analyze the global stability for a discrete-time predator-prey model which is discretized by a nonstandard finite difference scheme. Finally, an example with numerical simulation is given to demonstrate the effectiveness of the obtained results.

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Mathematics Subject Classification: Primary: 39A30; Secondary: 37J25, 92B99.

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