Dynamic Analysis Of Quaternion-valued Neural Networks

Quaternion-valued neural network(QVNN)is an extension of real-valued neural network(RVNN)and complex-valued neural network(CVNN),and has a wide range of applications in the fields of four-dimensional image,robot and human body image.Based on the existing conclusions,this paper studies the stability of two types of quaternion-valued neural network.The main contents are as follows:In the first chapter,the background and development of neural networks(mainly introducing recurrent neural networks,artificial neural networks based on impulsive control),quaternion and QVNNs are introduced.In the second chapter,the exponential input-to-state stability of QVNNs with time delay is discussed.In virtue of the quaternion multiplication is not suitable for commutative law,QVNN is resolved into four RVNNs.According to Lyapunov functional theory,sufficient condition for the system to reach exponential input-to-state stability are obtained.This conclusion is also applicable to QVNN without external input and CVNN with discrete delay.Finally,the validity of the conclusion is proved by two data simulations.In the third chapter,we study the global exponential stability of a class of quaternionvalued coupled neural networks.First,convert QVNN to the corresponding RVNN to avoid the non-commutative nature of quaternions when doing multiplication;secondly,by constructing appropriate Lyapunov function and using the matrix decomposition theorem,the sufficient criteria to ensure the global exponential stability of the systemare obtained;finally,some numerical simulations are given to prove the validity of the conclusions.The fourth chapter summarizes the main work of this article,discusses the shortcomings of the article and the direction of future research.