Periodic solutions of discrete-time Quaternion-valued BAM neural networks

Abstract

The existence and global asymptotic stability of periodic solutions for a class of discrete-time Quaternion-valued BAM neural networks are considered. Without using the estimate priori approach of periodic solutions, the fixed point theorem and the approach of combining a continuation theorem of coincidence degree theory with a Lyapunov sequence, without decomposing the discrete-time Quaternion-valued BAM neural networks into eight real-valued differential equations, by using a continuation theorem and constructing two Lyapunov sequences, the criterion to ensure the existence of periodic solutions for the considered networks is put forward. Next, by constructing two Lyapunov sequences, a criterion assuring the global asymptotic stability of periodic solutions of the quaternion-valued neural networks is achieved. Compared with the skills and results in the existing literature, our skills and results are completely new.