Singular perturbation analysis of competitive neural networks with different time scales.
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.
Institute for Flight Mechanics and Control, Darmstadt, Germany.
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Meyer-Bäse
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Ohl
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Scheich
D000465:Algorithms; D008959:Models, Neurological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D011336:Probability; D013997:Time Factors