The Almost Periodic Synchronization Of Several Classes Of Neural Networks

In the natural science and social science,almost periodicity is much more universal than periodicity.Motivated by the concept of periodic synchronization,in this dissertation,we study the almost periodic synchronization for the driveresponse system of several neural networks,and propose the concept of almost automorphic synchronization.By applying the Banach fixed point theorem and the exponential dichotomy of linear differential equations,four classical models of neural networks are investigated and the sufficient conditions for the existence of almost periodic solution(or almost automorphic solution)are obtained.Then based on the Lyapunov functional theories and some analytical technique,we obtain that the drive-response systems can realize global exponential synchronization.The results we obtained are completely new,and the method we employed can be used to study other synchronization problems of the neural networks,such as the weighted pseudo-almost periodic synchronization,pseudo-almost automorphic synchronization and weighted pseudo-almost automorphic synchronization.The whole dissertation is divided into six chapters.In Chapter 1,the background and history about the synchronization of neural networks are briefly addressed,and the main work of this dissertation are given.In Chapter 2,some basics related to the dissertation is presented.In Chapter 3,we investigate the almost periodic synchronization of a class of continuous neural networks,that is,the almost periodic synchronization of quaternion-valued shunting inhibitory cellular neural networks(QVSICNNs)with mixed delays.The sufficient condition for the existence of almost periodic solutions is obtained,and the sufficient criteria for the global exponential synchronization of the drive-response system under the state-feedback controller is constructed.Finally,a numerical simulation is given to verify the effectiveness and validity of the conclusions.In Chapter 4,as we all know,the automorphic function is the generalization of the almost periodic function,we study the almost automorphic synchronization of a class of continuous neural networks,that is,the almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks(QVHHNNs)with time-varying and distributed delays.The sufficient condition for the existence of almost automorphic solutions is obtained,and the sufficient criteria for the global exponential synchronization of the drive-response system under the state-feedback controller is constructed.Finally,a numerical simulation is given to verify the effectiveness and feasibility of the conclusions.In Chapter 5,we add an impulse term in the state-feedback controller,and discuss the almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control.We obtain the sufficient conditions for the existence of almost periodic solutions,and the sufficient criteria for the global exponential synchronization of the drive-response system is constructed.At last,a numerical simulation is given to show the feasibility of the conclusions.In Chapter 6,we design the system as an impulsive system,and investigate the almost periodic synchronization for the Clifford-valued Cohen-Grossberg neural networks with time-varying delays and impulse.By applying the analytical technique,we obtain the sufficient conditions for the existence of the piecewise almost periodic solution.Furthermore,we obtain the criteria for the global exponential synchronization of the drive-response system via state-feedback controller.Finally,a numerical simulation is given to show the feasibility of the conclusions.