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Zbl 1198.35033
Pan, Jie; Liu, Xinzhi; Zhong, Shouming
Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. (English)
[J] Math. Comput. Modelling 51, No. 9-10, 1037-1050 (2010). ISSN 0895-7177

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.

MSC 2000:: *35B40 Asymptotic behavior of solutions of PDE
35R10 Difference-partial differential equations
35K57 Reaction-diffusion equations
92B20 General theory of neural networks

Keywords: impulsive; time delay; Cohen-grossberg neural network; reaction-diffusion; global exponential stability; Poincaré inequality

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Zentralblatt MATH Berlin [Germany]