Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms

Two sufficient conditions, which ensure the existence and uniqueness of the equilibrium point and global exponential stability of bi-directional associative memory (BAM) neural networks with distributed delays and reaction-diffusion terms, are obtained by using the theory of topological degree, properties of M-matrix, Lyapunov functional, and analysis technique. The two sufficient conditions are independent of each other. The results remove the usual assumption that the activation functions are of bounded character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Two numerical examples are given to show the correctness of our analysis. These results can be applied to design globally exponentially stable networks and thus have important significance in both theory and applications.