## 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:

 34D23 Global stability of solutions to ordinary differential equations 92D25 Population dynamics (general) 92D30 Epidemiology 34C40 Ordinary differential equations and systems on manifolds

CNN
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### References:

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