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This paper investigates the origin of the threshold switching effect in niobium oxide based filamentary switching cells.

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SUMMARYA number of resistive switching memories exhibit activation-based dynamical behavior, which makes them suitable for neuromorphic and programmable analog filtering applications. Because the Boundary Condition Memristor (BCM) model accounts for tunable activation thresholds only at the on and off boundary states, it is not quantitatively accurate in the description of these kinds of memristors and in the investigation of their circuit applications. This paper introduces the Generalized Boundary Condition Memristor (GBCM) model, preserving the features of the BCM model while allowing, further, an ad-hoc tuning of activation-based dynamics, which enables an appropriate modulation of the conditions under which memristors may operate as storage elements or data processors. A simple circuit implementation of the novel model is presented, and time-efficient simulations confirming the improvement in modeling accuracy over the BCM model are shown. As a proof-of-concept for the suitability of the GBCM model in the exploration of the full potential of memristors in neuromorphic circuits and programmable analog filters, this paper adopts it to model fundamental synaptic rules governing the mechanisms of learning in neural systems and to gain some insight into key issues in the design of a couple of filters.

This work elucidates some aspects of the nonlinear dynamics of a thermally-activated locally-active memristor based on a micro-structure consisting of a bi-layer of and materials. Through application of techniques from the theory of nonlinear dynamics to an accurate and simple mathematical model for the device, we gained a deep insight into the mechanisms at the origin of the emergence of local activity in the memristor. This theoretical study sets a general constraint on the biasing arrangement for the stabilization of the negative differential resistance effect in locally active memristors and provides a theoretical justification for an unexplained phenomenon observed at HP labs. As proof-of-principle, the constraint was used to enable a memristor to induce sustained oscillations in a one port cell. The capability of the oscillatory cell to amplify infinitesimal fluctuations of energy was theoretically and experimentally proved.

The class of nonlinear dynamical systems known as memristive systems was defined by Chua and Kang back in 1976. Since then, many studies have addressed the search for physically-realisable memristive systems. In this reported work, it is proved that the class of memristive systems encloses an elementary electronic circuit comprising a full-wave rectifier with a second-order RLC filter.Introduction: The existence of a resistor endowed with memory was conjectured by Chua back in 1971 [1]. Just a few years later, Chua and Kang realised that the memory-resistor (memristor) is just one element from a class of nonlinear dynamical systems, the memristive systems, characterised, in general, by a state-dependent algebraic relation between input and output and by a system of ordinary differential equations governing the time evolution of the state [2]. Since then, scientists have devoted much effort in the search for physical realisations of memristive systems. In this field of research the most well-known breakthrough was undoubtedly achieved in 2008 at Hewlett-Packard (HP) Laboratories (Labs), where Williams recognised the first memristor nano-device [3]. Subsequently, a thorough experimental investigation of the switching dynamics of a set of metal-dioxide-metal memristive nano-devices [4] led to a better understanding of the key physical mechanisms underlying the nonlinear behaviour under observation. In 2011 we proposed a versatile boundary-condition-based model (BCM) for memristive switching nano-structures [5]. The BCM state equation includes a boundary-condition-controlled switching window function. The tunability of the window's switching mechanism allows the BCM to capture the nonlinear behaviour of a large class of memristive nano-films, including all dynamics attributed to the HP memristor and reported in [3]. Taking inspiration from the BCM switching function, we recently investigated the possibility to realise a memristive electronic system through switching networks, frequently used in power electronics applications. This investigation led us to prove that the Graëtz bridge with the RLC series filter is a memristive system. In particular, the proposed circuit manifests the fingerprint of memristive systems [6], i.e. a pinched hysteretic current-voltage loop for any state initial condition and for any nonzero amplitude and any nonzero and non-infinite frequency of any periodic sign-varying driving source. The peculiarity of our circuit is that it acts as a nonlinear resistor at direct current (DC) and at infinite frequency of any periodic sign-varying driving source with nonzero amplitude. It is a common belief that the only memristor realisations employing already-existing components are the complex topologies based upon the mutator-based active circuits presented in [1]. This circuit represents the first-ever realisation of a memristive electronic system using only passive components (four diodes, an inductor, a capacitor and a resistor).

One of the main issues preventing a large-scale exploration of the full potential of memristors in electrical circuits lies in the convergence issues and numerical errors encountered in the computer-aided integration of the differential algebraic equation set governing the peculiar dynamical behavior of these nonlinear two-terminal electrical components. In most cases the complexity of this equation set prevents an analytical derivation of closedform state solutions. Therefore the investigation of the nonlinear dynamics of memristors and circuits based upon them relies on software-based integration of the mathematical equations. In this paper, we highlight solution accuracy issues which may arise from an improper numerical integration of the equations, and then propose techniques addressing the problems properly. These guidelines represent a useful guide to engineers interested in the numerical analysis of memristor models.