中文摘要：

具有记忆功能的忆阻器是除电阻器、电容器和电感器之外的第四种基本二端电路元件.提出了由φ-q平面上的一条三次单调上升的非线性曲线来确定的光滑磁控忆阻器,它有着斜＂8＂字形的类紧磁滞回线的伏安特性曲线.采用此忆阻器和负电导构成的有源忆阻器替换蔡氏混沌电路中的蔡氏二极管,导出了一个基于忆阻器的混沌振荡电路.此外,利用常规的运算放大器和乘法器等元器件给出了有源忆阻器的等效电路实现形式.理论分析、数值仿真和电路仿真结果一致,均表明忆阻混沌电路的动力学行为依赖于忆阻器的初始状态,在不同初始状态下存在混沌振荡、周期振荡或稳定的汇等不同的运行轨道.

英文摘要：

Memristor with memory function is the fourth fundamental two-terminal circuit element,besides resistor,capacitor and inductor.In this paper,a smooth flux-controlled memristor is described by a monotone-increasing nonlinearity curve in the φ-q plane,and it has an italic type ＂8＂ like voltage current relation curve that looks like a pinched hysteresis loop characteristics.By replacing Chua＇s diode with an active memristor consisting of a smooth flux-controlled memristor and a negative conductance,a memristor based chaotic oscillation is derived from Chua＇s circuit.Furthermore,the equivalent circuit implementation form for the active memristor is designed by utilizing conventional components such as operational amplifiers and multipliers.The results from theoretical analysis,numerical simulations and circuit simulations are completely identical with each other,and demonstrate that the dynamical behaviors of the memristor chaotic circuit are dependent on the memristor initial state,showing different orbits such as chaotic oscillation,periodic oscillation and stable sink under different initial states.