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This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincar'e inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results. [ABSTRACT FROM AUTHOR]