Existence And Global Exponential Stability Of Periodic Solutions For Several Kinds Of Quaternion-valued Cellular Neural Networks

In this paper,without transforming the quaternion-valued cellular neural networks into four equivalent real-valued systems or two equivalent complex-valued systems,the existence and global exponential stability of periodic solutions for several kinds of quaternion-valued cellular neural networks with time-varying delays are investigated by direct method.By using the Mawhin continuation theorem of coincidence degree theory and constructing suitable Lyapunov function,firstly,we investigated the existence and global exponential stability of periodic solutions for quaternion-valued general cellular neural networks(QVCNNs)with time-varying delays.Secondly,we studied the existence and global exponential stability of periodic solutions for a kind of quaternion-valued shunting inhibitory cellular neural networks(QVSICNNs)with time-varying delays.Finally,we studied the existence and global exponential stability of periodic solutions for a kind of quaternion-valued Cohen-Grossberg cellular neural networks(QVCGCNNs)with time-varying delays.In addition,in order to illustrate the validity of the results,the corresponding examples are given for each chapter.Our results are new and our method can be used to study the existence and stability of periodic solutions for other types of neural network models.