Existence and global exponential stability of periodic solutions for quaternion-valued cellular neural networks with time-varying delays

In this paper, a class of quaternion-valued cellular neural networks (QVCNNs) with time-varying delays is considered. By using the continuation theorem of Mawhin's coincidence degree theory, the existence of periodic solutions for QVCNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of periodic solutions for QVCNNs. Finally, two examples are given to illustrate the effectiveness of the obtained results.