Dynamical Systems with Several Equilibria and Natural Liapunov Functions

Vladimir Rasvan

Address. Department of Automatics, University of Craiova, A.I. Cuza, 13, Craiova, 1100, Romania

E-mail: rasvan@automation.ucv.ro

Abstract. 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.

AMS classification. 34D20, 34A11

Key words. Several equilibria, qualitative behaviour, Liapunov function