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Several equilibria; qualitative behaviour; Liapunov function Introduction Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines; chemical reactions; economics; biology; neural networks
Several equilibria; qualitative behaviour; Liapunov function Introduction Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines; chemical reactions; economics; biology; neural networks
Summary:
Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines, chemical reactions, economics, biology, neural networks. As pointed out by many researchers, good results on qualitative behaviour of such systems may be obtained if a Liapunov function is available. Fortunately for almost all systems cited above the Liapunov function is associated in a natural way as an energy of a certain kind and it is at least nonincreasing along systems solutions.
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