Dynamics of bidirectional associative memory networks with distributed delays and reaction–diffusion terms

In this paper, the periodic oscillatory solution and stability are investigated for a class of bidirectional associative memory neural networks with distributed delays and reaction–diffusion terms. By constructing a new Lyapunov functional, applying M-matrix theory and inequality technique, several novel sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solutions for bidirectional associative memory neural networks with distributed delays and reaction–diffusion terms, and all other solutions of this network converge exponentially to the unique periodic oscillatory solution. Moreover, the exponential convergence rate is estimated, which depends on the delay kernel functions and the system parameters. Two numerical examples are given to show the effectiveness of the obtained results. The results extend and improve the previously known results.