Dynamical Analysis Of Memristor-based Fractional-order Neural Networks With Time Delay

In recent years,the fractional-order neural networks because of its good properties,has become an important subject in the research of nonlinear field.Compared with integer-order neural networks,the fractional-order neural networks provided a important tool for describing the overall function,and enhanced its capacity.In addition,Modeling of neu-rons involved in memristor can simulate the human brain nervous system more accurately.Besides,time delay is unavoidable in actual operating system,it can cause instability and even lead to chaos.In this paper,we proposed memristor-based fractional-order neural networks with time delay and analyzed its stability problem.The main work is as follows:1.The dynamical behaviors of the memristor-based fractional-order neural networks with time delay is investigated.Based on the theories of set-valued maps and differential inclusions,from the aspect of Filippov sense,by applying the fractional-order comparison theorem,the locally asymptotic stability conditions of the memristor-based fractional-order neural networks with time delay are obtained.Moreover,because the existence of measurement error and transmission noise,the bounded perturbation is unavoidable for the actual operating system,so the conditions for uniform stability of this system are given and its attractive interval is estimated.2.The performance of the control system is significantly impacted by the external interference,especially the parameter uncertainty,which can cause a gap between the theory and the practice.Moreover,most of the neural networks involve complex signals,and complex-valued neural networks have different and more complicated behaviors and varieties,so the memristor-based fractional-order complex-valued neural networks with time delay under parameter uncertainties should be taken into consideration seriously.Under Filippov sense,based on the fractional-order comparison theorem,M-matrix and the homomorphic theory,the existence of unique equilibrium is proved.On this basis,the conditions for the global asymptotic stability of this system have been obtained when its nonlinear activation function could be separated into its real and imaginary parts.Besides,the conditions for local asymptotic stability of this system have been acquired when the nonlinear activation function is bounded.