Pan, Jie; Liu, Xinzhi; Zhong, Shouming Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1198.35033 Math. Comput. Modelling 51, No. 9-10, 1037-1050 (2010). Summary: This paper studies impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays and Neumann boundary conditions. By employing the topological degree theory, delay differential inequality with impulses, linear matrix inequality (LMI) and Poincaré inequality, a set of sufficient conditions are derived to ensure the existence, uniqueness and global exponential stability of the equilibrium point. These global exponential stability conditions depend on the reaction-diffusion term. A comparison between our results and the previous results shows that our results establish a new set of stability criteria for reaction-diffusion neural networks and have improved the previous results. Cited in 33 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35R10 Partial functional-differential equations 35K57 Reaction-diffusion equations 92B20 Neural networks for/in biological studies, artificial life and related topics Keywords:impulsive; time delay; Cohen-grossberg neural network; reaction-diffusion; global exponential stability; Poincaré inequality PDF BibTeX XML Cite \textit{J. Pan} et al., Math. Comput. Modelling 51, No. 9--10, 1037--1050 (2010; Zbl 1198.35033) Full Text: DOI References: [1] Cohen, M.; Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst. Man Cybern., 13, 815-826 (1983) · Zbl 0553.92009 [2] Cao, J.; Liang, L., Boundedness and stability for Cohen-Grossberg neural network with time-varying delays, J. Math. Anal. 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