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Global asymptotic stability of a class of dynamical neural networks
Anke Meyer-Bäse1, Sergei S Pilyugin
1Department of Electrical and Computer Engineering, Florida State University, Tallahassee, FL 32310-6046, USA.
Abstract:
The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.
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