Theoretical Foundations of Memristor Cellular Nonlinear Networks: Memcomputing With Bistable-Like Memristors

Tetzlaff, Ronald; Ascoli, Alon; Messaris, Ioannis; Chua, Leon O.

doi:10.1109/tcsi.2019.2940909

Cited by 60 publications

(37 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…X, referred to as an equilibrium for the memristor state Equations (3) and (7), with state evolution function expressed by formula (5) and ( 9), under the specified bias voltage (current) stimulus V m (I m ), indicates a possible DC operating point for the memristor state in this scenario. Finally, it is worth mentioning that, recently, the DRM graphical tool has been extended to nonlinear dynamical systems with two degrees of freedom (Tetzlaff et al, 2020), which shall allow, for example, an in-depth study of the nonlinear dynamics of second-order memristors. 037 mA, 49.296 mA].…”

Section: Drm-and Circuit-theoretic Based Investigations Of the Device DC Responsementioning

confidence: 99%

“…While the most economically profitable application field of these two-terminal devices is the non-volatile memory sector (Mikolajick et al, 2009;Ielmini and Waser, 2016), their inherently rich dynamical behavior allows to use them alternatively for sensing or processing data. Their peculiar capability to merge a number of different functionalities locally makes them the key nanotechnology enabler toward the future hardware implementation of novel ground-breaking information processing paradigms, including in-memory-computing (Ielmini and Wong, 2018), bio-inspired mem-computing (Di Ventra and Traversa, 2018;Xia and Yang, 2019;Ascoli et al, 2020bAscoli et al, ,c, 2021Tetzlaff et al, 2020), and bio-sensing (Tzouvadaki et al, 2016(Tzouvadaki et al, , 2020 strategies.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Local Activity and Edge of Chaos in a NaMLab Memristor

et al. 2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Drm-and Circuit-theoretic Based Investigations Of the Device DC Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Local Activity and Edge of Chaos in a NaMLab Memristor

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…We have x(t) = ϕ C 1 (t; t 0 ), y(t) = (ϕ C 2 (t; t 0 ), q L (t; t 0 )) T and w(t) = q C 1 (t; t 0 ), z(t) = (q C 2 (t; t 0 ), ϕ L (t; t 0 )) T , where T denotes the transpose. Then, on the basis of (10), (11) we obtain that the modified Chua's circuit satisfies the following third-order system of SEs in the (ϕ, q)-domaiṅ…”

Section: Chua's Circuit With Memristormentioning

confidence: 99%

Unfolding Nonlinear Dynamics in Analogue Systems With Mem-Elements

Marco

Forti

Corinto

et al. 2021

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

The paper considers a relevant class of networks containing memristors and (possibly) nonlinear capacitors and inductors. The goal is to unfold the nonlinear dynamics of these networks by highlighting some main features that are potentially useful for real-time signal processing and in-memory computing. In particular, an analytic treatment is provided for dynamic phenomena as the presence of invariant manifolds, the coexistence of different regimes, complex dynamics and attractors and the phenomenon of bifurcations without parameters, i.e., bifurcations due to changing the initial conditions of the state variables for a fixed set of circuit parameters. The paper also addresses the issue of how to design pulse independent voltage or current sources to steer the network dynamics through different manifolds and attractors. Two relevant examples are worked out in details, namely, a variant of Chua's circuit with a memristor and a nonlinear capacitor and a relaxation oscillator with a memristor and a nonlinear inductor. In the latter example, the paper also studies the effect on manifolds and coexisting dynamics when real memristive devices are accounted for using a class of extended memristor models. The analysis is conducted by means of a recently developed technique named flux-charge analysis method (FCAM). Numerical simulations are presented to confirm the theoretic findings.

show abstract

“…However, as is the case here, converting traditional nonlinear circuits to memristive equivalents may require the extension of classical nonlinear system-theoretic techniques. The Memristor Cellular Nonlinear Network (M-CNN), proposed in Tetzlaff et al (2020), differs from a standard time-and space-invariant two-dimensional CNN (Chua and Yang, 1988a;Chua and Yang, 1988b), characterized by first-order cells, and typically implemented in hardware (Vázquez et al, 2018), for the inclusion of a single nonvolatile memristor in parallel to the capacitor in the circuit implementation of each processing element. One of the most powerful tools for the analysis of nonlinear dynamical systems with one degree of freedom is the Dynamic Route Map (DRM) (Chua, 2018a), which represents the system-theoretic technique of reference for the investigation of CNNs with first-order processing elements.…”

Section: Introductionmentioning

confidence: 99%

“…Since the memristive cell in the proposed M-CNN features two degrees of freedom, the investigation of the cellular array calls for the generalization of the DRM graphical tool, applicable to first-order systems only. The modified DRM graphical tool, applicable to second-order dynamical systems, is known as Second-Order Dynamic Route Map (DRM 2 ) (Tetzlaff et al, 2020). The application of this novel system-theoretic technique to the model of the proposed M-CNN allows to gain a deep insight into the rich nonlinear behaviour of its second-order processing elements, unveiling dynamical phenomena, which may not emerge in the original cellular array (Ascoli et al, 2020b).…”

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Theoretical Foundations of Memristor Cellular Nonlinear Networks: Memcomputing With Bistable-Like Memristors

Cited by 60 publications

References 24 publications

On Local Activity and Edge of Chaos in a NaMLab Memristor

On Local Activity and Edge of Chaos in a NaMLab Memristor

Unfolding Nonlinear Dynamics in Analogue Systems With Mem-Elements

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

Contact Info

Product

Resources

About