Global exponential stability of bidirectional associative memory neural networks with distributed delays

Abstract

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality a ∏ k = 1 m b k q k ⩽ 1 r ( ∑ k = 1 m q k b k r + a r ) ( a ⩾ 0 , b k ⩾ 0 , q k > 0 with ∑ k = 1 m q k = r - 1 , and r > 1 ), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.