Synchronization Control Of Two Types Of Memristive Neural Networks With Time-varying Delays

Synchronization is a common phenomenon in nature,and it is widespread in the fields of biology,physics,chemistry,engineering technology,society and economy.In recent decades,the synchronization of neural networks has become a hot issue in the academic community.This article mainly considers the synchronization behavior of two types of memristive neural networks with time-varying delays.These two types of neural networks can be understood as first-order and second-order neural networks,as well as real-valued and quaternion-valued neural networks.This article mainly discusses the asymptotic synchronization of the fuzzy second-order memristive neural network,the exponential synchronization of the quaternionvalued memristive neural network and the second-order quaternion-valued memristive neural network.In this paper,using second-order neural networks non-reduced order method,quaternion-valued neural networks non-decomposing method,and some inequality techniques,the sufficient conditions for the corresponding algebraic inequality form are obtained by constructing appropriate Lyapunov functionals.Finally,some numerical simulation examples are given to prove the correctness of the theoretical results.The full text is mainly summarized in the following five parts:Chapter 1 is the introduction,which firstly introduces the background,purpose and significance of the research,then introduces the research background of neural networks,followed by a brief overview of the research status of memristive neural networks,quaternion-valued neural networks and second-order neural networks.In Chapter 2,the asymptotic synchronization problem of fuzzy second-order memristive neural networks with time-varying and infinitely distributed delays is studied by constructing state feedback and adaptive control schemes and using the non-reduced order method.On the basis of Lyapunov stability theory,Barbalat Lemma and some analysis strategies,several new criteria in light of algebraic inequalities are acquired to ensure the asymptotic synchronization of the concerned models.In Chapter 3,the exponential synchronization of delayed memristive quaternion-valued neural networks under quantized intermittent control is studied.Without decomposing the original systems into usual real-valued or complex-valued ones,the discussed system is processed in both cases of the differential inclusion theory.Based on two kinds of quantized intermittent control strategies,and by applying Lyapunov funtional method and some inequality techniques,several new delay-dependent criteria in the form of real-valued algebraic inequalities are derived to ensure the global exponential synchronization of the concerned system.Compared with the traditional feedback control,the quantized intermittent control strategy can reduce control cost and shorten the time to reach synchronization.The fourth chapter is based on the third chapter to study the exponential synchronization problem of second-order memristive quaternion-valued neural networks with neutral type and mixed delay.Instead of using the traditional order reduction method or the traditional decomposition method for the second-order system and the quaternion-valued system,this chapter study the system as a whole.By constructing some new Lyapunov-Krasovskii functionals and applying some inequalities,several new exponential synchronization criteria in the form of algebraic inequalities are proposed by hybrid switched control.The results obtained in this chapter are not only limited to the quaternion field,but also extended to the complex and the real number field.The fifth chapter mainly makes a comprehensive summary of the work of the whole paper,and gives the problems that need to be further studied in order to continue the research.