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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)