Pattern Formation With Locally Active S-Type NbO<sub>x</sub> Memristors

Weiher, Martin; Herzig, Melanie; Tetzlaff, Ronald; Ascoli, Alon; Mikolajick, Thomas; Slesazeck, Stefan

doi:10.1109/tcsi.2019.2894218

Cited by 47 publications

(20 citation statements)

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“…Since the potassium and sodium ion channels in biological axon membranes (Hodgkin and Huxley, 1952) are locally active memristors (Chua et al, 2012), which provide an essential contribution for the emergence of the all-ornone neuronal spiking behavior, it is clear that solid-state resistance switching memories, which admit a negative smallsignal resistance over a range of operating points, which, as explained in this manuscript, constitutes a signature for their capability to enter the LA domain, will play a major role for the development of basic electronic building blocks of novel biomimetic neuromorphic networks. There have already been a few promising attempts to adopt these kinds of memristor physical realizations (Pickett and Williams, 2012) for the electronic implementation of biological neurons, the so-called neuronal memristors, or neuristors for short Yi et al, 2018), which have been further combined through various coupling arrangements to form memristive cellular automata endowed with computational universality , and memristive cellular neural networks (M-CNNs), which, supporting the emergence of dynamic patterns (Weiher et al, 2019;Demirkol et al, 2021), may be employed to solve complex non-deterministic polynomial-time (NP)-hard optimization problems, such as the challenging task of coloring the vertices of an undirected graph (Weiher et al, 2021). In this article, we employed powerful techniques from non-linear circuit (Chua, 1987) and system (Ascoli et al, 2019;Corinto et al, 2020) theory as well as rigorous concepts from the theory of complexity to gain a thorough understanding of the non-linear dynamics of a locally active memristive microstructure from NaMLab.…”

Section: Discussionmentioning

confidence: 99%

“…Superimposing a small-signal on top of the DC operating point, the locally active memristor may operate similarly as a MOS transistor biased in the saturation region, amplifying the local fluctuations at the expense of some DC power supply. Besides opening up the opportunity to design transistor-less small-signal amplification circuits as well as oscillatory networks, in which the emergence of spatiotemporal phenomena (Weiher et al, 2019) may be exploited to solve complex optimization problems (Weiher et al, 2021), the adoption of locally active memristors in electronics may also allow an accurate reproduction of the non-linear dynamics of potassium and sodium ion channels in innovative 35 It is instructive to observe that even the ion channels in the human heart (Zhang et al, 2020) are volatile locally active memristors. neuromorphic hardware .…”

Section: Discussionmentioning

confidence: 99%

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On Local Activity and Edge of Chaos in a NaMLab Memristor

et al. 2021

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Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state volatile memory devices, which, biased through appropriate DC sources, may enter a local activity domain, and, most importantly, the associated stable yet excitable sub-domain, referred to as edge of chaos, which is where the seed of complexity is actually planted, is of great appeal to the neuromorphic engineering community. This paper applies fundamentals from the theory of local activity to an accurate model of a niobium oxide volatile resistance switching memory to derive the conditions necessary to bias the device in the local activity regime. This allows to partition the entire design parameter space into three domains, where the threshold switch is locally passive (LP), locally active but unstable, and both locally active and stable, respectively. The final part of the article is devoted to point out the extent by which the response of the volatile memristor to quasi-static excitations may differ from its dynamics under DC stress. Reporting experimental measurements, which validate the theoretical predictions, this work clearly demonstrates how invaluable is non-linear system theory for the acquirement of a comprehensive picture of the dynamics of highly non-linear devices, which is an essential prerequisite for a conscious and systematic approach to the design of robust neuromorphic electronics. Given that, as recently proved, the potassium and sodium ion channels in biological axon membranes are locally active memristors, the physical realization of novel artificial neural networks, capable to reproduce the functionalities of the human brain more closely than state-of-the-art purely CMOS hardware architectures, should not leave aside the adoption of resistance switching memories, which, under the appropriate provision of energy, are capable to amplify the small signal, such as the niobium dioxide micro-scale device from NaMLab, chosen as object of theoretical and experimental study in this work.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

On Local Activity and Edge of Chaos in a NaMLab Memristor

et al. 2021

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“…Thereafter, the mathematical and physical locally active memristive devices have attracted increasing attention from scientific and technological communities. There is evidence that the locally active memristors [50][51][52] have intense nonlinearity and complicated dynamics due to its rich equilibria stability. At present, the locally active memristor models with one or two stable pinched hysteresis loops under different initial states have been reported.…”

Section: Introductionmentioning

confidence: 99%

Firing multistability in a locally active memristive neuron model

et al. 2020

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The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the construced neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.

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“…CNNs process information through the analogue dynamics of the cells' states, which converge toward distinct attractors depending upon inputs and/or initial conditions. While wavebased computing, where the cellular array carries out data processing tasks through the generation of specific dynamic patterns, is an active field of research (Weiher et al, 2019), there exists a huge library (Karacs et al, 2018) of image processing operations, which the nonlinear dynamic array may execute as the cells' states approach predefined equilibria. This paper focuses on the performance of CNNs (M-CNNs) as equilibria-based computing (mem-computing) engine.…”

Section: Introductionmentioning

confidence: 99%

System-Theoretic Methods for Designing Bio-Inspired Mem-Computing Memristor Cellular Nonlinear Networks

Ascoli

Tetzlaff

Kang

et al. 2021

Front. Nanotechnol.

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The introduction of nano-memristors in electronics may allow to boost the performance of integrated circuits beyond the Moore era, especially in view of their extraordinary capability to process and store data in the very same physical volume. However, recurring to nonlinear system theory is absolutely necessary for the development of a systematic approach to memristive circuit design. In fact, the application of linear system-theoretic techniques is not suitable to explore thoroughly the rich dynamics of resistance switching memories, and designing circuits without a comprehensive picture of the nonlinear behaviour of these devices may lead to the realization of technical systems failing to operate as desired. Converting traditional circuits to memristive equivalents may require the adaptation of classical methods from nonlinear system theory. This paper extends the theory of time- and space-invariant standard cellular nonlinear networks with first-order processing elements for the case where a single non-volatile memristor is inserted in parallel to the capacitor in each cell. A novel nonlinear system-theoretic method allows to draw a comprehensive picture of the dynamical phenomena emerging in the memristive mem-computing array, beautifully illustrated in the so-called Primary Mosaic for the class of uncoupled memristor cellular nonlinear networks. Employing this new analysis tool it is possible to elucidate, with the support of illustrative examples, how to design variability-tolerant bio-inspired cellular nonlinear networks with second-order memristive cells for the execution of computing tasks or of memory operations. The capability of the class of memristor cellular nonlinear networks under focus to store and process information locally, without the need to insert additional memory units in each cell, may allow to increase considerably the spatial resolution of state-of-the-art purely CMOS sensor-processor arrays. This is of great appeal for edge computing applications, especially since the Internet-of-Things industry is currently calling for the realization of miniaturized, lightweight, low-power, and high-speed mem-computers with sensing capability on board.

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Pattern Formation With Locally Active S-Type NbO_x Memristors

Cited by 47 publications

References 23 publications

On Local Activity and Edge of Chaos in a NaMLab Memristor

On Local Activity and Edge of Chaos in a NaMLab Memristor

Firing multistability in a locally active memristive neuron model

System-Theoretic Methods for Designing Bio-Inspired Mem-Computing Memristor Cellular Nonlinear Networks

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Pattern Formation With Locally Active S-Type NbOx Memristors

Cited by 47 publications

References 23 publications

On Local Activity and Edge of Chaos in a NaMLab Memristor

On Local Activity and Edge of Chaos in a NaMLab Memristor

Firing multistability in a locally active memristive neuron model

System-Theoretic Methods for Designing Bio-Inspired Mem-Computing Memristor Cellular Nonlinear Networks

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Pattern Formation With Locally Active S-Type NbO_x Memristors