Stability Analysis Of Neutral Quaternion-valued Neural Network

Quaternion valued neural networks have been widely application in quantum mechanics and computer graphics.In particular,Quaternion valued neural networks can process multi-layer information through multi-state activation functions.Therefore,the research on its stability and anti-periodic solutions has become a very hot topic.In this paper,we establish the global asymptotic stability of a class of Quaternion valued Bidirectional Associative Memory(BAM)neural networks and the asymptotic stability of anti-periodic solutions.Firstly,this paper introduces the domestic and foreign scholars' research status and main research methods of Quaternion valued BAM neural networks.Meanwhile,the paper gives the concept of Quaternion valued and the definition of stability and the lemma needed for the research work.Secondly,considering that most scholars used the decomposition method to conduct research in the past,this paper does not decompose the Quaternion valued BAM neural network system into four real valued systems,but employ direct research on the system.With the help of homeomorphism theorem and differential inequality technique,and using proof by contradiction,the existence of the equilibrium point of the Quaternion valued BAM neural network is given.Secondly,by constructing a new Lyapunov function,sufficient conditions for the global asymptotic stability of the equilibrium point of the neural network are given.When discussing the asymptotic stability of anti-periodic solution of Quaternion valued BAM neural network,the continuation theorem of coincidence degree theory,uniqueness theorem of differential equation solution,Schwartz inequality,integral inequality and other techniques are used to avoid decompositions of the neural network into real valued systems.The existence and asymptotic stability of the anti-periodic solution are obtained by constructing the Lyapunov function which is different from the existing literature.Finally,two numerical verifications are given to illustrate the correctness of the theory.