This paper presents a novel current-controlled locally-active memristor model to reveal the switching and oscillating characteristics of locally-active devices. It is shown that the memristor has two asymptotically stable equilibrium points on its power-off plot and therefore exhibits nonvolatility. Switching from one stable equilibrium point to another is achieved by applying a suitable current pulse. The locally-active characteristic of the memristor is measured by the DC I–V plot. A small-signal equivalent circuit on a locally-active operating point with the bias current I is constructed for describing the characteristic of the locally-active region of the memristor. A periodic oscillator circuit composed of the locally-active memristor, a compensation inductor and a resistor is proposed, whose dynamics is analyzed in detail by using the Hopf bifurcation and the zeros and poles of the impendence function of the circuit. It is found that the locally-active memristor based circuit with different current biases or different initial conditions can exhibit different dynamics such as periodic oscillation and stable equilibrium point. If an energy storage element (capacitor) is added to the periodic oscillation circuit, a chaotic oscillator is obtained, which can exhibit abundant dynamics. The oscillation mechanism of the memristor-based oscillator is analyzed via dynamic route map (DRM), showing that the memristor is an essential device for generating periodic and chaotic oscillations, and its local activity is the cause for complex oscillations.

中文翻译：

---

双稳态电流控制局部有源忆阻器的动力学

本文提出了一种新颖的电流控制局部有源忆阻器模型，以揭示局部有源器件的开关和振荡特性。结果表明，忆阻器在断电图上有两个渐近稳定的平衡点，因此表现出非易失性。通过施加合适的电流脉冲实现从一个稳定平衡点到另一个平衡点的切换。忆阻器的局部有源特性由直流测量一世–五阴谋。具有偏置电流的局部有源工作点上的小信号等效电路一世构造用于描述忆阻器局部有源区的特性。提出了一种由局部有源忆阻器、补偿电感和电阻组成的周期振荡电路，利用Hopf分岔和电路阻抗函数的零点和极点对其动力学进行了详细分析。研究发现，具有不同电流偏置或不同初始条件的基于局部有源忆阻器的电路可以表现出不同的动态特性，例如周期性振荡和稳定平衡点。如果在周期振荡电路中加入一个储能元件（电容器），就得到了一个混沌振荡器，它可以表现出丰富的动态特性。基于忆阻器的振荡器的振荡机制通过动态路由图 (DRM) 进行分析，