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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
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2.21

Neural Computation

November 15, 1996, Vol. 8, No. 8, Pages 1731-1742
(doi: 10.1162/neco.1996.8.8.1731)
© 1996 Massachusetts Institute of Technology
Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales
Article PDF (473.07 KB)
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.