Existence And Global Exponential Stability Of Periodic Solutions And Anti-periodic Solutions For Two Types Of Quaternion-valued Neural Networks

In this thesis,we discuss the existence and global exponential stability of periodic solutions and anti-periodic solutions for two classes of quaternion-valued neural networks.Some new results are obtained.Where,in the second chapter,by combining the continuation theorem of Mawhin's coincidence degree theory,the existence of periodic solutions for a class of quaternion-valued cellular neural networks(QVCNNs)with time-varying delays is studied,and by constructing a suitable Lyapunov function,we prove the global exponential stability of periodic solutions for QVCNNs.In the third chapter,by using a new continuation theorem of coincidence degree theory,we study the existence of antiperiodic solutions for a class of quaternion-valued high-order Hopfield neural networks(QVHHNNs)with time-varying delays,and by constructing an appropriate Lyapunov function,some sufficient conditions are derived to guarantee the global exponential stability of anti-periodic solutions for this networks.Finally,several examples are given to illustrate the effectiveness of the obtained result.