SINGULAR PERTURBATION ANALYSIS OF COMPETITIVE NEURAL NETWORKS WITH DIFFERENT TIME SCALES

The dynamics of complex neural networks must include the aspects of lo ng- and short-term memory. The behavior of the network is characterize d by an equation of neural activity as a fast phenomenon and an equati on of synaptic modification as a slow part of the neural system. The m ain idea of this paper is to apply a stability analysis method of fixe d points of the combined activity and weight dynamics for a special cl ass of competitive neural networks. We present a quadratic-type Lyapun ov function for the now of a competitive neural system with fast and s low dynamic variables as a global stability method and a modality of d etecting the local stability behavior around individual equilibrium po ints.