Dimensionality reduction modeling and characteristic analysis of memristive circuit

Abstract

Through mathematical modeling analysis of Chua’s memristive circuit, the problem of dimensionality reduction for dynamical modeling of memristive circuit is proposed. Taking memristive circuit with two memristors for example, dimensionality reduction modeling of the memristive circuit is performed, on which a three-dimensional system model is established. Based on this model, the equilibrium points and stabilities are analyzed, and the dynamical characteristics, when the parameters are varied, are investigated. Furthermore, the analysis results from the conventional model are compared with the results from the dimensionality reduction model of memristive cicuit with two memristors. The results indicate that the dimensionality of the dimensionality reduction model of memristive circuit is related to the number of capacitors and inductors only, but unrelated to the number of memristors; there exist nonlinear phenomena about the coexistence of bifurcation modes in the memristive circuit when circuit parameters are varied; the dimensionality reduction modeling reduces the complexity of system modeling, which is conducive to dynamical charateristic analysis of the system but eliminates the effect of the initial conditions of the memristors internal state variables on dynamical charateristics of memristive circuit.