<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, P. O. Box 59911, Abu Dhabi, UAE

Department of Mathematics & Statistics, College of Science, P. O. Box 36, Sultan Qaboos University, Muscat 123, SULTANATE OF OMAN

Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, BULGARIA

Zlatinka Covacheva Middle East College, Muscat, SULTANATE OF OMAN

Higher College of Telecommunications and Post, Sofia, BULGARIA

Tatra Mountains Mathematical Publications

An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré...

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

Online veröffentlicht: 04. Juli 2013

Seitenbereich: 1 - 18

DOI: https://doi.org/10.2478/tmmp-2013-0001

This content is open access.