Global-stability problem for coupled systems of differential equations on networks

被引：706
作者：
Li, Michael Y. [1 ]
Shuai, Zhisheng [1 ]
机构：
[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 01期
基金：
加拿大自然科学与工程研究理事会; 加拿大创新基金会;
关键词：
Coupled systems of differential equations; Dynamical systems on networks; Lyapunov functions; Global stability; Kirchhoff's Matrix Tree Theorem; TIME DELAYS; MODELS; DISPERSAL; DYNAMICS;
D O I：
10.1016/j.jde.2009.09.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The global-stability problem of equilibria is investigated for coupled systems of differential equations on networks. Using results from graph theory, we develop a systematic approach that allows one to construct global Lyapunov functions for large-scale coupled systems from building blocks of individual vertex systems. The approach is applied to several classes of coupled systems in engineering, ecology and epidemiology, and is shown to improve existing results. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1 / 20
页数：20
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