Finite/Fixed-time Synchronization Control Of Memoristor-based Delayed Neural Networks

In 1971,Chua first predicted the existence of memristors(the abbreviation of memory resistor)theoretically.A prototype of memristor was manufactured firstly by Hewlett-Packard Lab in 2008.From then on it was attractive for scholars to research memristor-based neural networks.As an important part of the behavior of dynamic systems,there is a lot of papers which are concern about the synchronization of dynamic systems,including asymptotic synchronization,exponential synchronization,finite-time synchronization,fixed-time synchronization and so on.Designing different controllers is one of the hot topics to guarantee finite/fixed-time synchronization of drive-response system.Memristor-based neural networks is one of the functional differential equations with discontinuous right-hand sides,and we consider the corresponding functional differential inclusions by Filippov regularization method.This paper investigates finite/fixed-time synchronization of memristor-based delayed neural networks,by constructing the appropriate inequality and Lyapunov functional.Sufficient conditions are established to guarantee finite/fixed-time synchronization of drive-response system via two types of controllers.The main results of this paper are as follows:First,we introduce the concept,research significance,and the progress of memristor.Then the research status of memristor-based delayed neural networks,state feedback control and adaptive control are summarized.Finally,propaedeutics of this paper are given,including the introduction of mathematic model,some definitions,assumptions and lemmas.Then we discuss drive-response system finite/fixed-time synchronization of memristor-based delayed neural networks,by designing state feedback controllers.Sufficient conditions are established to realize finite/fixed-time synchronization,and the proposed results are easy to verify.Finally we study the finite/fixed-time synchronization of memristor-based delayed neural networks based on the derive-response concept.Sufficient conditions are established by using adaptive controllers to guarantee finite/fixed-time synchronization of drive-response system.The numerical simulations are given to show the validity of results.