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Flow invariance for competitive multi-modal neural networks

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

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.

Published in:

Neural Networks, 2003. Proceedings of the International Joint Conference on  (Volume:4 )

Date of Conference:

20-24 July 2003