Research On The Synchronization And Stability Of Several Class Quaternion-Valued Neural Networks

In recent years,the dynamics behavior of neural networks(NNs)has been received a lot of research results,but these reports are mainly concentrated on real-valued NNs and complex-valued NNs.Different from real and plural,the multiplication of quaternions does not satisfy the commutation law,the existing results of the dynamic analysis for realvalued NNs and complex-valued NNs cannot be directly applied to the quaternion-valued neural networks(QVNNs),so the research of quaternion-valued neural networks is a very challenging topic.In this dissertation,we mainly studied the synchronization control of two types of delayed QVNNs and the stability of neutral-type quaternion-valued neural networks(QVNTNNs).The main works are as follows:(1)The exponential anti-synchronization problem of quaternion-valued neural networks with time delays is considered.Firstly,the exponential anti-synchronization problem of the above neural networks is converted to exponential stability problem of corresponding error system.Next,the error system is decomposed into four real-valued systems by decomposition techniques.By using a suitable Lyapunov function and inequality theory,a simple controller is designed and some sufficient conditions are achieved to ensure anti-synchronization of drive-response system.(2)The fixed-time synchronization problem of quaternion-valued Cohen-Grossberg neural networks with time-varying delays is considered.In the case of system is treated as an entirety without any decomposition,by the properties of sign function related to quaternion and inequality techniques,a suitable feedback controller and the Lyapunov function are designed,some sufficient conditions are acquired to guarantee the fixed-time synchronization of the discussed network.(3)The global asymptotic stability of quaternion-valued neutral-type neural networks with time-varying delays is studied.Firstly,the quaternion-valued neural networks are converted into equivalent real-value neural networks by decomposition method,then using homeomorphism theorem,the existence and uniqueness of the equilibrium point of the system are proved.At last,some criteria are obtained to ensure the global asymptotic stability of the discussed system.