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Zbl 1190.34063
Li, Michael Y.; Shuai, Zhisheng
Global-stability problem for coupled systems of differential equations on networks. (English)
[J] J. Differ. Equations 248, No. 1, 1-20 (2010). ISSN 0022-0396

Authors' abstract: 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 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.
[Fozi Dannan (Damascus)]

MSC 2000:: *34D23 Global stability
92D25 Population dynamics
92D30 Epidemiology
34C40 ODE on manifolds

Keywords: coupled systems of differential equations; dynamical systems on networks; Lyapunov functions; global stability; Kirchhoff's matrix tree theorem

Cited in: Zbl pre06092804

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