Research On Analytical Method Of Fractional-order Memristor Circuit Based On Volterra Series

Memristor,as the fourth basic circuit element besides resistance,capacitance and inductance,represents the relationship between charge and flux which are two basic variables in the basic circuit theory.Memristor is a kind of nonlinear resistance with memory function,because of its unique nonlinear characteristics,memristor have great potential application in the fields of secure communication and neural network.Volterra series is a kind of mathematical function which describes the relationship between input and output of nonlinear system,it can represent the essential characteristics of nonlinear system.Therefore,it is of great significance to study fractional-order memristor circuit by using Volterra series.Based on the detailed analysis of the existing nonlinear circuit analysis methods,a method of modeling and analyzing fractional-order memristor circuit based on Volterra series is proposed,and the circuit with fractional-order memristor is constructed.The analytic solution of fractional-order memristor circuit under different order is obtained by using this analytic method,The mathematical simulation of the analytical results is carried out by Matlab software,which verifies the correctness of the method.At the same time,the method of fractional-order memristor circuit analysis based on convolution operation is analyzed,the advantages and disadvantages of the two methods in the analysis of fractional-order memristor circuits are compared and summarized.The Spice model of fractional-order memristor is introduced in detail,and the Spice circuit of fractional-order memristor are constructed.the output voltage and current of the fractional-order memristor circuit with different fractional order are obtained by Pspice software simulation.The characteristic curve of the fractional-order memristor is studied,and the results of the mathematical simulation are compared with Matlab software,The experimental results show that the simulation results of the two methods are similar,which verifies the correctness of the proposed method.