Research On Synchronization Control Of Two Classes Of Fractional Order Complex Networks

In human society and nature world,many complex systems can be regarded as complex networks processing.In recent years,fractional-order calculus has become a hot research topic with the advantages of me mory and heredity.Therefore,it is necessary to study fractional complex networks.Many attentions have been paid to synchronization which is an important dynamic behavior of complex networks.Besides,synchronization control is widely used in secure communication,smart grid,neural network and other fields.This paper studies the finite-time synchronization control problem of a class of fractional-order complex networks and the Mittag-Leffler synchronization control problem of a class of fractional-order memristor neural networks respectively.For finite-time synchronization problem of a class of fractional-order coupled heterogeneous complex networks with time-varying delays and external disturbances,a new lemma for finite-time stability of fractional-order complex networks is presented based on fractional calculus theory.By using this original lemma and some common inequalities,the simple and easy-to-implement feedback controller and the adaptive controller with better performance are designed respectively.What's more,the sufficient conditions for the finite-time synchronization of the fractional complex networks are obtained.Finally,two numerical examples are given to illustrate the correctness and effectiveness of the results.For Mittag-Leffler synchronization problem of a class of fractional-order memristor-based neural networks with time-varying delays and leakage delays,based on fractional-order calculus theory,differential inclusion theory and Mittag-Leffler stable fractional-order Lyapunov method,the sufficient conditions for achieving Mittag-Leffler synchronization of the fractional-order memristor-based neural networks are obtained by using feedback control method and adaptive control method.It is novel to use adaptive control method to solve the Mittag-Leffler synchronization problem of fractional-order memristor-based neural networks.Finally,two numerical examples are given to illustrate the correctness and effectiveness of the results.