Complexity and abundant dynamics may arise in locally-active systems only, in which locally-active elements are essential to amplify infinitesimal fluctuation signals and maintain oscillating. It has been recently found that some memristors may act as locally-active elements under suitable biasing. A number of important engineering applications would benefit from locally-active memristors. The aim of this paper is to show that locally-active memristor-based circuits can generate periodic and chaotic oscillations. To this end, we propose a non-volatile locally-active memristor, which has two asymptotically stable equilibrium points (or two non-volatile memristances) and globally-passive but locally-active characteristic. At an operating point in the locally-active region, a small-signal equivalent circuit is derived for describing the characteristics of the memristor near the operating point. By using the small-signal equivalent circuit, we show that the memristor possesses an edge of chaos in a voltage range, and that the memristor, when connected in series with an inductor, can oscillate about a locally-active operating point in the edge of chaos. And the oscillating frequency and the external inductance are determined by the small-signal admittance Y(iω). Furthermore, if the parasitic capacitor in parallel with the memristor is considered in the periodic oscillating circuit, the circuit generates chaotic oscillations.

复杂性和丰富的动态可能仅出现在局部活跃的系统中，其中局部活跃的元素对于放大无穷小的波动信号和保持振荡至关重要。最近发现一些忆阻器可以在适当的偏置下充当局部有源元件。许多重要的工程应用将受益于本地有源忆阻器。本文的目的是表明基于局部有源忆阻器的电路可以产生周期性和混沌振荡。为此，我们提出了一种非易失性局部有源忆阻器，它具有两个渐近稳定的平衡点（或两个非易失性忆阻器）和全局无源但局部有源的特性。在局部活跃区域的一个工作点，推导了一个小信号等效电路，用于描述忆阻器工作点附近的特性。通过小信号等效电路，我们证明了忆阻器在一个电压范围内具有混沌边缘，当忆阻器与电感串联时，可以在边缘处的局部有源工作点附近振荡。混乱。并且振荡频率和外部电感由小信号导纳决定Y (i ω )。此外，如果在周期振荡电路中考虑与忆阻器并联的寄生电容，则电路会产生混沌振荡。