Flow invariance for competitive neural networks with different time-scales

Abstract

The dynamics of complex neural networks must include the aspects of long and short-term memory. The behaviour of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a method of analyzing the dynamics of a system with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory.