一阶器件、混合忆阻器和非线性电路理论的前沿
First order devices, hybrid memristors, and the frontiers of nonlinear circuit theory
摘要：
近年来，在非线性电路理论中出现了几种具有记忆效应的器件。其中，这些电路元件包括蔡氏忆阻器，以及忆电容器和忆电感器。这些和其他相关器件似乎超出了电路理论的经典范围，电路理论是用电阻器、电容器、电感器以及电压和电流源来表述的。在本文中，我们探讨了潜在的非线性电路理论的程度进行分类，这样的MEM设备中所涉及的变量在其本构关系和概念的微分和状态顺序的设备。在这个框架内，一阶电路理论的前沿是由所谓的混合忆阻器定义的，这里提出混合忆阻器以适应与所有四个基本电路变量相关的特性。具有二阶微分的器件和MEM系统的讨论不太详细。我们考虑了所有电路元件的完全非线性特性，得出了一个相当详尽的C^1-器件分类。此外，我们扩展的概念的拓扑退化配置的电路与memcapacitors，memindicators和所有类型的忆阻器，并表征这种电路的节点模型的微分代数指数。
英文摘要：
Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices seem to be beyond the, say, classical scope of circuit theory, which is formulated in terms of resistors, capacitors, inductors, and voltage and current sources. We explore in this paper the potential extent of nonlinear circuit theory by classifying such mem-devices in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. Within this framework, the frontier of first order circuit theory is defined by so-called hybrid memristors, which are proposed here to accommodate a characteristic relating all four fundamental circuit variables. Devices with differential order two and mem-systems are discussed in less detail. We allow for fully nonlinear characteristics in all circuit elements, arriving at a rather exhaustive taxonomy of C^1-devices. Additionally, we extend the notion of a topologically degenerate configuration to circuits with memcapacitors, meminductors and all types of memristors, and characterize the differential-algebraic index of nodal models of such circuits.
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