First order devices, hybrid memristors, and the frontiers of nonlinear circuit theory

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.Comment: Published in 2013. Journal reference included as a footnote in the first pag

Robust Simulation of a TaO Memristor Model

This work presents a continuous and differentiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in software. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable functions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable approximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal candidates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit simulator

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page

Everything You Wish to Know About Memristors But Are Afraid to Ask

This paper classifies all memristors into three classes called Ideal, Generic, or Extended memristors. A subclass of Generic memristors is related to Ideal memristors via a one-to-one mathematical transformation, and is hence called Ideal Generic memristors. The concept of non-volatile memories is defined and clarified with illustrations. Several fundamental new concepts, including Continuum-memory memristor, POP (acronym for Power-Off Plot), DC V-I Plot, and Quasi DC V-I Plot, are rigorously defined and clarified with colorful illustrations. Among many colorful pictures the shoelace DC V-I Plot stands out as both stunning and illustrative. Even more impressive is that this bizarre shoelace plot has an exact analytical representation via 2 explicit functions of the state variable, derived by a novel parametric approach invented by the author

Toward bio-inspired information processing with networks of nano-scale switching elements

Unconventional computing explores multi-scale platforms connecting molecular-scale devices into networks for the development of scalable neuromorphic architectures, often based on new materials and components with new functionalities. We review some work investigating the functionalities of locally connected networks of different types of switching elements as computational substrates. In particular, we discuss reservoir computing with networks of nonlinear nanoscale components. In usual neuromorphic paradigms, the network synaptic weights are adjusted as a result of a training/learning process. In reservoir computing, the non-linear network acts as a dynamical system mixing and spreading the input signals over a large state space, and only a readout layer is trained. We illustrate the most important concepts with a few examples, featuring memristor networks with time-dependent and history dependent resistances