Anti-synchronization Of Memristor-based Fractional-Order Neural Networks

As a special dynamic system,neural dynamic system is a hot research topic in recent years.Most of what we see are integer-order dynamic systems.However,in real life,it requires the system to be of arbitrary order.So,research on fractional-order system has good application value.This paper analyzes the problem of anti-synchronization of fractional-order memristor-based neural networks with fractional orderα belong to 0<α<1,several kinds of linear feedback controllers are designed,and the sufficient conditions for the neural network are obtained by using the discontinuous dynamical system theory,the Laplace transform,the Mittag-Leffler function method and the Leibniz rules.Moreover,it is demonstrated by the numerical simulation.Firstly,this paper introduces the research background,purpose and significance of fractional-order memristor-based neural networks,some concepts and models of this paper are presented.And then,we give the main work of this paper.Secondly,two kinds of linear feedback controllers are designed.By using the theory of fractional-order differential equations with discontinuous right-hand side,Laplace transform and Mittag-Leffler function,results are derived to guarantee the global Mittag-Leffler anti-synchronization of fractional-order memristor-based neural networks.And we use the numerical simulation to verify the effectiveness of the results.Thirdly,by using the theory of fractional-order differential equations with discontinuous right-hand side,and Leibniz rules,the sufficient conditions for global O(t-α)anti-synchronization of fractional-order memristor-based neural networks are obtained under the appropriate linear feedback controllers.Then,we use the numerical simulation to verify the effectiveness of the results.At last,we make a summary,and put forward some problems which can be studied further.