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Global exponential stability of competitive neural networks with different time scales

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3 Author(s)
Meyer-Baese, A. ; Dept. of Electr. & Comput. Eng., Florida State Univ., Tallahassee, FL, USA ; Pilyugin, S.S. ; Chen, Y.

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of such a neural 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 new method of analyzing the dynamics of a biological relevant 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, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.

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Neural Networks, IEEE Transactions on  (Volume:14 ,  Issue: 3 )