Equivalent Modeling And Dynamical Analysis Of Memristive Circuit

Memristo r, a nonlinear resistor with memory property realized physically r ecentl y, is the fourth basic two-terminal circuit element. In this paper, based on Taylor seri es form of φ-q relationship, a charge-controlled memri stor eq uivalent ci rcuit analysis model was built. A c harge-con trolled memristo r model with cubic n onlineari ty was taken as an example to per form theo retical an alysis of circui t characteristics, s uch as voltage-current r elationship,activ e-passive property and so on, of the charge-controlled memristor ? ?under different parame ter s The results indicat e t hat the voltage-current r elationsh ip of the charge-controlled me mristor has italic "8" shaped hys ter esis loop char a cter istic, and the charge-cont rolled memristor presents passivity and acti v ity accompanied with t he var iat ions of parameter symbols,r esulting in the occurrence of the corr esponding variations of circu it ch aracteristics, which are wel l verified by equi v alent circuit. Compared with the pas sive memr istor, t he activ e memristor is mo re suitable for used as a second har monic signal generati on circu it.Furthermore, based on the physical attributes of magnetic flux and ch arge, two circuit laws wa s reconstru cted and the flux-charge relations o f three fundamental circuit elements was establish ed, and a novel mapping eq uivalent ap proach wa s proposed. The map p ing equivalent approach illustrates that a memristor bas ed dy namical circu it can be analyze d and r eal ized equivalently by a nonlinear dynamical cir cuit with the same topol o gy an d circuit parameters. A memri stor based chaotic circuit and th e co rres pon ding Chu a’s chaoti c circu it with two ou tput differentiators wer e taken as example s to i llustrate this approach. Equivalent dynamical an alysis an d realizati o n of the memristor based chaotic cir cuit were performed by using Ch ua’s chaotic circuit. The r esults indicate that the outputs of memris tor based chaotic circuit and t h e co rres ponding outputs of Chua’s chaotic ci rcuit have identical dynamic s. The proposed appr oach v erified by numerical simulations and experimen tal observations is useful to designs and analyses of memristor based dynamic al circui ts.