Global exponential stability of impulsive delayed reaction-diffusion neural networks via Hardy-Poincarè inequality

Authors:
Yutian Zhang;Qi Luo
Affiliations:
College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 21004, China;College of Information & Control, Nanjing University of Information Science & Technology, Nanjing 21004, China
Venue:
Neurocomputing
Year:
2012

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Abstract

This work addresses the stability of impulsive cellular neural networks with time-varying delays and reaction-diffusion terms. By means of Hardy-Poincare inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize, under mild conditions, some new and concise algebraic criteria ensuring the global exponential stability of the equilibrium point. The provided stability criteria are true to Dirichlet boundary condition and concerned with the reaction-diffusion coefficients, the regional feature and the first eigenvalue of the Dirichlet Laplacian. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.