Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1198.35033

Pan, Jie; Liu, Xinzhi; Zhong, Shouming

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.

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

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