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Dynamical systems with several equilibria and natural Lyapunov functions. (English) Zbl 0915.34043

The paper is devoted to dynamical systems with several equilibria and their asymptotic behaviour. First, some basic concepts are recalled, such as monostability and quasi-monostability of systems, gradient-like systems, quasi-gradient-like systems and pointwise globally stable systems. The author emphasizes the role of Lyapunov functions, the existence of which may simplify the task of showing that the \(\omega\)-limit sets are composed of equilibria only. Several applications from chemical kinetics, from biology and from neural networks are given together with convenient Lyapunov functions associated in a natural way as an energy of certain kind.
Reviewer: J.Kalas (Brno)

MSC:

34D20 Stability of solutions to ordinary differential equations
37-XX Dynamical systems and ergodic theory
34C11 Growth and boundedness of solutions to ordinary differential equations
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