中文摘要：

忆阻器（memristor）是一种有记忆功能的非线性电阻器,它是除电阻器、电容器和电感器之外的第四种基本电路元件.采用一个具有光滑磁控特性曲线的忆阻器和一个负电导替换蔡氏振荡器中的蔡氏二极管,导出了一个基于忆阻器的振荡器电路.采用常规的动力学分析手段研究了电路参数和初始条件变化时该光滑忆阻振荡器的动力学特性.研究结果表明,光滑忆阻振荡器与一般的混沌系统完全不同,它的动力学行为除了与电路参数有关外,还极端依赖于电路的初始条件,存在瞬态混沌和状态转移等奇异的非线性物理现象.

英文摘要：

Memristor,which is a nonlinear resistor with memory function,is the fourth fundamental two-terminal circuit element besides the resistor,capacitor and inductor. A memristor based oscillator circuit,directly derived from Chua＇s oscillator by replacing Chua＇s diode with a flux-controlled memristor characterized by a smooth monotonically increasing nonlinearity,is presented in this paper. By using conventional dynamical analysis method,the dynamical behaviors of the new smooth memristor oscillator with the variations of circuit parameters and initial conditions are investigated. The research results demonstrate that the dynamical behavior of the smooth memristor oscillator not only depends on the circuit parameters,but also closely depends on the initial conditions of the circuit. Different from general chaotic systems,some novel nonlinear phenomenas,such as the transient chaos and state transitions and so on,can be found in the proposed system.