Equivalent Circuit Implementation Of Meminductor And Modeling Analyses Of Memristive Circuits

Due to the Physical realizability of memristor，kinds of applicationcircuits have been widely studied by people. Meminductor is theoreticallydeduced from the memristor and it’s a new two-port nonlinear circuitelement with memory function. This paper will review the origin ofmemristor and meminductor, and give the definition of these twoelements, then analysis the equivalent circuit implementation of memorycomponents and the modeling of memristor chaotic circuit.In this paper, based on the model of meminductor approximateequivalent circuit, and by utilizing an active flux-controlled memristorcharacterized by smooth cubic nonlinearity to realize the memristor in theequivalent circuit, a state equation set of the meminductor approximateequivalent circuit is established. With the help of MATLAB mathematicaltool software, the properties of the equivalent meminductor are analyzednumerically. The results indicate that the flux-current relations of theequivalent meminductor typically behave as a pinched hysteresis loopcharacteristics and depend on the frequencies of applied voltage stimulus.By using the equivalent circuit of active flux-controlled memristor, theexperimental verification for meminductor approximate equivalent circuitis performed. The experimental measurement results agree essentiallywith numerical simulation results, which illustrate that the model ofmeminductor approximate equivalent circuit is effective.Through mathematical modeling analysis of Chua’s memristivecircuit, the problem of dimensionality reduction for dynamical modelingof memristive circuit is proposed. Taking memristive circuit with twomemristors as an example, dimensionality reduction modeling of thememristive circuit is performed, upon which a three dimensional systemmodel is established. Based on this model, the equilibrium points arecalculated and stabilities are analyzed, at the same time the dynamicalcharacteristics with the variations of parameters are investigated.Furthermore, the analysis results from the conventional model and thedimensionality reduction model of memristive cicuit with two memristorsare compared. The results indicate that the dimensionality of thedimensionality reduction model of memristive circuit is only related to the number of capacitors and inductors and not related to the number ofmemristors; there exist nonlinear phenomena of the coexisting bifurcationmodes in the memristive circuit with the variations of circuit parameters;the dimensionality reduction modeling reduces the complexity of systemmodeling, which is help to dynamical charateristic analysis of the system,but eliminates the effect of the initial conditions of the memristorsinternal state variables on dynamical charateristics of memristive circuit.