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Global-stability problem for coupled systems of differential equations on networks. (English) Zbl 1190.34063
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.

MSC:
34D23Global stability of ODE
92D25Population dynamics (general)
92D30Epidemiology
34C40ODE on manifolds
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