Dynamical Behaviors Of Memristive Neural Networks And Quaternion-valued Neural Networks

Artificial neural networks are with the characteristics such as high rate of fault tolerance,strong self-learning ability,parallel computing and so on.It is the foundation of machine learning and one of the most important implement of artificial intelligence.Moreover,it has been successfully applied in deep learning,optimal computation,and associative memory,etc.Therefore,the research of neural networks has become a hot topic among scholars.The dynamical behavior of memristive neural networks and quaternion-valued neural networks are discussed in this doctoral thesis.This thesis consists of six main chapters.The dynamical behavior of memristive neural networks is investigated in the second chapter.The stability of quaternion-valued neural networks is studied in the third chapter.In the fourth chapter,the asymptotic synchronization and event-triggered synchronization of quaternion-valued neural networks are discussed.In the fifth chapter,the fixed-time synchronization of quaternionvalued memristive neural networks is explored.Conclusions of this thesis are given briefly in the sixth chapter.Further details are listed as following:In Chapter 2,firstly,through a nonlinear transformation,we derive an alternative system from the considered memristor-based Cohen-Grossberg neural networks.By designing both feedback controller and constructing comparison systems,a sufficient condition is derived to guarantee the fixed-time synchronization of drive-response system with impulsive effects.Secondly,we investigate the fixed-time output synchronization of coupled reaction-diffusion neural networks(CRDNNs).In addition,the output delayed coupling and discontinuous activations are taken into consideration.With the Lyapunov functional and fixed-time control theory,a novel feedback control scheme is proposed to guarantee fixed-time output synchronization of the considered CRDNNs.In Chapter 3,firstly,we investigate the Lagrange global exponential stability of quaternionvalued memristive neural networks(QVMNNs).Two kinds of activation functions are considered.Then,based on the Lyapunov function approach,decomposition method and some inequality skills,two novel sufficient conditions for the lagrange stability of QVMNNs are provided corresponding to different kinds of activations.Secondly,the stochastic disturbance is introduced into the QVMNNs.Then,the exponential input-to-state stabilization(EISS)problem of stochastic QVMNNs is investigated.In order to be more effective and less costly in real applications,an event-triggered control strategy is adopted.Then,making use of the Lyapunov function approach and stochastic analysis technique,novel sufficient conditions for mean square EISS of stochastic QVMNNs are derived.Later,it is proved that the Zeno behavior does not occur in our control scheme.In Chapter 4,firstly,the problem of drive-response global synchronization of QVMNNs is investigated.Two cases are taken into consideration,one is with the conventional differential inclusion assumption,the other without.Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques.Secondly,the event-triggered synchronization of QVMNNs is investigated.With the designing of event-triggered strategy and sampled controller,corresponding synchronization criteria are then derived based on Lyapunov method.Moreover,it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy.In Chapter 5,firstly,based on the differential inclusion principle and the Lyapunov functional method,fixed-time synchronization is considered in the form of drive-response system for QVMNNs.A novel fixed-time controller is designed to achieve the control goal.With the fixed-time stability theory and some inequality techniques,criterion for fixed-time synchronization for QVMNNs is given.Secondly,by introducing inertial term into QVMNNs,the model of QVIMNNs is established.The problem of fixed-time synchronization of the QVIMNNs is investigated based on the variable transformation and Lyapunov functional method.Two types of activation functions are considered,and novel criteria guaranteeing fixed-time synchronization for each cases are then derived.In Chapter 6,conclusions of this thesis are summarized briefly,and several subjects which deserve further study are given.