Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 248, Issue 1, Pages 1-20Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2009.09.003
Keywords
Coupled systems of differential equations; Dynamical systems on networks; Lyapunov functions; Global stability; Kirchhoff's Matrix Tree Theorem
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Funding
- Natural Science and Engineering Research Council of Canada (NSERC)
- Canada Foundation for Innovation (CFI)
- Izaak Walton Killam Memorial Scholarship at the University of Alberta
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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.
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