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

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
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### References:

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