Synchronization Control Of Coupled Fractional-order Neural Networks With Time Delay

In the past few decades,many scholars have paid more and more attention to the study of fractional calculus.With the development of science and technology,fractional calculus theory is becoming more and more mature.As we all know,the fractional calculus is extended based on integer order calculus,it has been widely used in many fields,such as biology,physics,engineering and so on.The synchronization control of fractional-order neural dynamics has been a hot and difficult research topic.This paper mainly investigates some fractional-order neural networks systems,including the fractional-order neural networks,coupled fractional order neural networks,fractional-order complex networks.By using fractional Mittag-Leffler function method,comparison principle and Razumikhin stability theorem,several sufficient conditions of neural network systems synchronization are derived.The main contents of this paper include:The multi-quasi-synchronization problem of coupled fractional-order neural networks with delays is investigated.By utilizing the pinning impulsive strategy,a novel controller is designed to pin the coupled networks to realize the multi-quasi-synchronization.Based on the comparison principle and mathematical analysis,some novel criteria of the multi-quasi-synchronization are derived.Moreover,the effects of coupling strength and pinning control matrix are discussed.Two numerical simulations are presented to demonstrate the effectiveness of the obtained results.The pinning and adaptive synchronization problem of fractional-order complex dynamical networks with time-varying delay is discussed.By designing two suitable feedback controllers,and utilizing Razumikhin-type stability theory and matrix inequality technique,some novel criteria of the pinning synchronization and pinning adaptive synchronization are derived.Two numerical simulations are presented to demonstrate the effectiveness of the obtained results.The synchronization problem for two classes of coupled fractional-orderreaction-diffusion neural networks with time-varying delay is studied.The two types of systems nodes are coupled by their delayed states and delayed spatial diffusion terms,respectively.By applying Razumikhin-type stability theory and Mittag-Leffler stability,some novel criteria of the synchronization are derived.Finally,two numerical simulations are presented to demonstrate the effectiveness of the obtained results.