Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality

This work is devoted to the investigation of stability theory for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks with Dirichlet boundary condition. By means of Hardy–Poincarè inequality and Gronwall–Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring global exponential stability of the equilibrium point. The presented stability criteria show that not only reaction–diffusion coefficients but also regional features as well as the first eigenvalue of the Dirichlet Laplacian will impact the stability. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

► Impulsive delayed reaction–diffusion Cohen–Grossberg neural networks are studied. ► We firstly use Hardy–Poincarè inequality to deal with the reaction–diffusion terms. ► Gronwall–Bellman-type impulsive integral inequality is used for the stability study. ► The presented stability criteria are related to the diffusion regional features.