Singular perturbation analysis of competitive neural networks with different time scales

Authors:
Anke Meyer-Bäse;Frank Ohl;Henning Scheich
Affiliations:
Institute for Flight Mechanics and Control, Petersenstrasse 30, 64287 Darmstadt, Germany;Federal Institute for Neurobiology, Brenneckestrasse 6, 39118 Magdeburg, Germany;Federal Institute for Neurobiology, Brenneckestrasse 6, 39118 Magdeburg, Germany
Venue:
Neural Computation
Year:
1996

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Abstract

The dynamics of complex neural networks must include the aspects of long-and short-term memory. The behavior 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. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points.