Stability Analysis Of Memristor-based Fractional-order Hopfield Neural Networks With Parameter Disturbances

The fractional calculus,as a subject of studying non-integer calculus,is the general-ization of the integer calculus to arbitrary real number order.The fractional-order neural networks,compared with the integer-order neural networks,can better describe the prop-erties of the systems and can also better simulate the human's brain.On the other hand,the memristor,as the new forth perfect electrical element,enjoys alterable resistance,and the memristor-based neural networks can better describe the properties of the human's brain.Compared with the integer-order neural networks,the theoretical study results of fractional-order neural networks and the memristor-based neural networks are relatively few,so plenty of significant work remains to be studied.As a result,the memristor-based fractional-order neural networks are a field of great potential deserving research.At the same time,we have considered the uncertainty of the system under the influence of the external factor,and analyzed the stability and synchronization of the system investigated with parameter uncertainties.The paper mainly focuses on the stability analysis of memristor-based fractional-order Hopfield neural networks with parameter disturbances.The definite work of the paper is as follows:1.The stability of memristor-based fractional-order Hopfield neural networks with parameter disturbances is investigated,and we have further studied the robust of the sys-tem.In this paper,the simplified model investigated is given first and the parameter un-certainties with respect to the external disturbance are taken into consideration.With the help of the fractional-order stability method,some conditions of realizing the stability are obtained.Specially,for such system which has the discontinuous right-hand sides,we have considered the existence and uniqueness of the solution.2.The synchronization of memristor-based fractional-order Hopfield neural network-s with parameter disturbances is investigated,and we also have further studied the robust of the master-slave system.In this paper,the simplified master-slave systems investigated are given first and the parameter uncertainties with respect to the external disturbance are taken into consideration.The closure arithmetic is employed to handle the error system,based on the suitable Lyapunov function and assumptions,the Mittag-Leffler stability of the error system is gotten by using the fractional-order stability method,so the error system is asymptotic stability,implying the master-slave system have realized the syn-chronization,due to the parameters disturbances,the conclusion that the system is robust has been obtained.