忆阻电路降维建模与特性分析

通过对蔡氏忆阻电路的数学建模分析,提出了忆阻电路动力学建模的降维问题.以包含两个磁控忆阻器的忆阻电路为例,进行了忆阻电路降维建模,由此建立了一个三维系统模型.基于该模型,分析了忆阻电路的平衡点和稳定性,研究了电路参数变化时忆阻电路的动力学特性.进一步,对包含两个磁控忆阻器的忆阻电路常规模型的分析结果和其降维模型的分析结果进行了比较.结果表明:忆阻电路降维模型的维数只与电容器的数量和电感器的数量有关,而与忆阻器的数量无关;当电路参数变化时忆阻电路存在分岔模式共存等非线性现象;降维建模降低了系统建模复杂度,有利于系统的动力学特性分析,但消除了忆阻器内部状态变量的初始条件对忆阻电路动力学特性的影响.

Dimensionality reduction modeling and characteristic analysis of memristive circuit

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.