Dynamic Analysis Of A Class Of Fractional-order Discontinuous Neural Network Systems

The fractional order calculation is a generalization of integer order calculation to any real order calculation,and compared with the integer order neural networks,the fractional order neural networks are widely used in physics,engineering,biology and so on because their higher degrees of freedom and memory characteristics.This paper consider the memristor based neural networks,which can better simulate the biology neural systems of human brain.In addition,the time delay and impulse phenomenon are taken into account in the neural networks model,for they are inevitable in life,such as the time delay in information transmission,the weather change in a short time and so on.So the stability and lag synchronization of a class of fractional-order discontinuous neural network systems are considered hereof:1.For a given memristor based fractional order neural network system with time delay,due to the noise generated by the system transmission and the error caused by the measurement are inevitable in life,so the bounded disturbance is considered in this paper.In addition,complex signals are usual problems in such systems,so the paper considered the system in complex field.In the sense of Filippov,By the principle of fixed points,the existence and uniqueness of the solution of the system is studied.Further by fractional order comparison theory and the second Lyapunov method discusses the asymptotic stability of the solution of the system.2.The lag synchronization of multiple discontinuous fractional order neural networks systems is considered hereof.The multiple neural networks consist of more than two neural networks and the time delay exists between two adjacent systems,which is different from the drive-response systems people usually studied.What's more,the leakage time delay also considered.The primary method is the second Lyapunov method.And in the sense of Filippov,by fractional order comparison theory and inequality scaling skills,the sufficient conditions of the lag synchronization of multiple discontinuous fractional order neural networks systems are given.