Improved Stability Estimates for Impulsive Delay Reaction-Diffusion Cohen-Grossberg Neural Networks Via Hardy-Poincaré Inequality

Improved Stability Estimates for Impulsive Delay Reaction-Diffusion Cohen-Grossberg Neural Networks Via Hardy-Poincaré Inequality

An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré inequality instead of Hardy-Sobolev inequality or just the nonpositivity of the reaction-diffusion operators, under suitable conditions in t...

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Veröffentlicht in:Tatra Mountains mathematical publications 2013-04, Vol.54 (1), p.1-18
Hauptverfasser: Akça, Haydar, Covachev, Valéry, Covacheva, Zlatinka
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Cohen-Grossberg neural networks
Hardy-Poincaré inequalit
impulses
reaction-diffusion
S-type delays
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description An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré inequality instead of Hardy-Sobolev inequality or just the nonpositivity of the reaction-diffusion operators, under suitable conditions in terms of M-matrices which involve the reaction-diffusion coefficients and the dimension and size of the spatial domain, improved stability estimates for the system with zero Dirichlet boundary conditions are obtained. Examples are given.
doi_str_mv 10.2478/tmmp-2013-0001
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subjects Cohen-Grossberg neural networks
Hardy-Poincaré inequalit
impulses
reaction-diffusion
S-type delays
title Improved Stability Estimates for Impulsive Delay Reaction-Diffusion Cohen-Grossberg Neural Networks Via Hardy-Poincaré Inequality
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