含忆阻器的并联混沌电路动力学分析

Dynamic Analysis of Parallel Chaotic Circuit with Memristor

忆阻器在保密通信、图像加密中具有重要应用价值。本文提出一种有源压控忆阻器,将该忆阻器和电容、电感并联构成了一个基于忆阻器的并联混沌电路,建立了该系统的无量纲数学模型。采用基本动力学分析方法对系统进行分析,计算了该电路的Lyapunov指数和Lyapunov维数,通过数值仿真得出该系统的相轨图和Poincaré映射,分析了系统的平衡点稳定性,采用Lyapunov指数谱和分岔图等分析方法,研究了电路参数改变对系统动力学行为产生的影响。数值仿真和理论分析结果表明,该系统可以产生一类特殊的超混沌吸引子,并且随着电路参数的变化产生复杂的非线性动力学行为。

Memristor has important application value in secure communication and image encryption.In this paper,an active voltage-controlled memristor is proposed.Based on the active memristor,a memristor chaotic circuit is constructed,and the dimensionless mathematical model of the circuit is derived.To analyze the dynamical characteristic of the system,we calculate the Lyapunov exponent and Lyapunov dimension,simulate the phase portrait and Poincarémapping,analyze the stability of the equilibrium.Furthermore,the dynamical behavior of the system is analyzed by the methods of Lyapunov exponent spectrum and bifurcation diagram.The numerical simulation and theoretical analyses show that the system produces a special chaotic attractor and exhibits nonlinear dynamical behavior with the change of circuit parameters.