Alon Ascoli

Nonlinear Dynamics of Memristor Oscillators

A thorough investigation of the nonlinear dynamics of networks of memristor oscillators is a key step towards the design of systems based upon them, such as neuromorphic circuits and dense nonvolatile memories. A wide gamut of complex dynamic behaviors, including chaos, is observed even in a simple network of memristor oscillators, proposed here as a good candidate for the realization of oscillatory associative and dynamic memories. A detailed study of number and stability of all periodic and nonperiodic oscillations appearing in the network may not leave aside a preliminary deep understanding of the local and global behavior of the basic oscillator. Depending on two bifurcation parameters, controlling memristor nonlinearity, the oscillator exhibits different dynamic behaviors, analyzed here through application of state-of-the-art techniques from the theory of nonlinear dynamics to the oscillator model.

A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures

A deep theoretical discussion proves that in Joglekars and Bioleks models the memductance-flux relation of a memristor driven by a sign-varying voltage source may only exhibit single-valuedness and multi-valuedness respectively. This manuscript derives a novel boundary condition-based Model for memristor nanostructures. Unlike previous models, the proposed one allows for closed-form solutions. More importantly, subject to the nonlinear behavior under exam, this model enables a suitable tuning of boundary conditions, which may result in the detection of both single-valued and multi-valued memductance-flux relations under certain sign-varying inputs of interest. The large class of modeled dynamics include all behaviors reported in the legendary paper revealing the existence of memory-resistance at the nano scale.

Memristor Model Comparison

Since the 2008-dated discovery of memristor behavior at the nano-scale, Hewlett Packard is credited for, a large deal of efforts have been spent in the research community to derive a suitable model able to capture the nonlinear dynamics of the nano-scale structures. Despite a considerable number of models of different complexity have been proposed in the literature, there is an ongoing debate over which model should be universally adopted for the investigation of the unique opportunities memristors may offer in integrated circuit design. In order to shed some light into this passionate discussion, this paper compares some of the most noteworthy memristor models present in the literature. The strength of the Pickett?s model stands in its experiment-based development and in its ability to describe some physical mechanism at the origin of memristor dynamics. Since its parameter values depend on the excitation of the memristor and/or on the circuit employing the memristor, it may be assumed as a reference for comparison only in those scenarios for which its parameters were reported in the literature. In this work various noteworthy memristor models are fitted to the Picketts model under one of such scenarios. This study shows how three models, Bioleks model, the Boundary Condition Memristor model and the Threshold Adaptive Memristor model, outperform the others in the replica of the dynamics observed in the Picketts model. In the second part of this work the models are used in a couple of basic circuits to study the variance between the dynamical behaviors they give rise to. This analysis intends to make the circuit designers aware of the different behaviors which may occur in memristor-based circuits according to the memristor model under use.

Analysis of current–voltage characteristics for memristive elements in pattern recognition systems

A topologically simple memristive-based oscillatory network showing a wide plethora of dynamical behaviors may be a good candidate for the realization of innovative oscillatory associative and dynamic memories for the recognition of spatial–temporal synchronization states. The design of such pattern recognition systems may not leave aside a preliminary thorough investigation of the nonlinear dynamics of the network and its basic components. In a synchronization scenario with almost-sinusoidal oscillations, each of the memristive elements used in the cells of the network under consideration features an unusual current–voltage behavior. This manuscript models the linear circuitry and the memristive element in each cell so as to capture the observed dynamics and then presents an analytical study explaining the quantitative dependence of memristive current–voltage behavior on excitation amplitude–angular frequency ratio and on initial condition on the system state. This work leads to the first rigorous classification of all possible current–voltage characteristics for a sine-wave voltage-driven memristive element. This analytical study shall pave way towards a better understanding of the complex and still unexplored dynamical properties of this nonlinear device, whose distinct features could improve the capabilities of future-generation pattern recognition systems. Copyright

Nonlinear Dynamics of a Locally-Active Memristor

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 Nb2O5 and Nb2Ox 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.

Generalized boundary condition memristor model

SUMMARY A 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. Copyright

Physical model of threshold switching in NbO2 based memristors

This paper investigates the origin of the threshold switching effect in NbO2. It is found that the effect is independent of the metal-insulator-transition but can be explained by a trap-assisted Frenkel–Poole like conduction mechanism in combination with a moderate temperature increase by only 150 K due to Joule heating. These findings lead to the development of a physics based model which is of pure electrical nature and explains the occurrence of the threshold effect as well as the negative-differential resistance behavior observed in NbO2.

A class of versatile circuits, made up of standard electrical components, are memristors

Summary In this paper, we propose a whole class of memristor circuits. Each element from the class consists of the cascade connection between a static nonlinear two-port and a dynamic one-port. The class may be divided into two subclasses depending on the input variable (voltage or current). Within each of these subclasses, two further sets of memristor circuits may be distinguished according to which output voltage and current of the two-port represents one of the system states. The simplest memristor circuits make only use of purely passive elementary components from circuit theory, an absolute novelty in this field of research. Thus they are suitable circuit primers for the introduction of the topic of memristors to undergraduate students. A sample circuit is built using discrete devices and its memristive nature is validated experimentally. In case the one-port is purely passive, the proposed circuits feature volatile memristive behavior. Allowing active devices into the dynamic one-port, non-volatile dynamics may also emerge, as proved through concepts from the theory of nonlinear dynamics. Given the generality of the proposed class, the topology of the emulators may be adjusted so as to induce a large variety of dynamical behaviors, which may be exploited to accomplish new signal processing tasks, which conventional circuits are unable to perform. Copyright

The Art of Finding Accurate Memristor Model Solutions

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 closed-form 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.

History Erase Effect in a Non-Volatile Memristor

This work presents a detailed study of the nonlinear dynamics of a tantalum oxide memristor recently fabricated at Hewlett Packard Labs. Our investigations uncover direct current, quasi-static, and alternating current behavior of the nanodevice. A thorough study of the dynamics emerging in the nanoscale element under various input/initial condition combinations reveals a fundamental property of the tantalum oxide device, which was unnoticed so far. The initial condition has no effect on the steady-state operation of the memristor under non-zero input. This property, known as fading memory in system theory, implies the uniqueness of asymptotic behavior of the memristor. The progressive input-induced memory erase phenomenon is solely determined by the switching dynamics of the nanodevice, mathematically described by the state evolution function, which governs the rate of evolution of the memristor state. A constant-sign DC input will activate on or off switching dynamics only. Consequently, due to the limited on/off memductance ratio, the memristor will asymptotically attain a fully-conducting or highly-resistive state, irrespective of the initial condition. Most interestingly, under AC periodic excitations, it is the pronounced asymmetry in the state dependence of on and off switching processes which is at the basis of the reported history erase effect. It is important to point out that this novel fading memory phenomenon does not compromise the nonvolatile behavior of the nanostructure. In fact, despite the device may be stimulated so as to forget its past history, it still has a continuum of analog nonvolatile memory states.