Theoretical Foundations of Memristor Cellular Nonlinear Networks: Stability Analysis With Dynamic Memristors

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

doi:10.1109/tcsi.2019.2957813

Cited by 54 publications

(29 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…denotes an additional M-CNN cell equilibrium in the linear region (Ascoli et al, 2020b). From the first M-CNN cell ODE Eq.…”

Section: Application Of the M-cnn Design Methodology To Execute Fundamental Memcomputing Tasksmentioning

confidence: 99%

“…In other words, under no circumstances may the respective SDP host one and only one globally asymptotically stable equilibrium (Strogatz, 2000). Table 2 sums up (Ascoli et al, 2020b) the location and local stability property of each equilibrium, which the M-CNN cell C(i, j) may admit under zero offset current depending upon the self-feedback synaptic weight a 0,0 .…”

Section: Zero Offset Current Scenariomentioning

confidence: 99%

“…Specifying the values 32 , reported in Table 3, for all the fixed parameters of the cell circuit of Figure 8, the viewgraphs in plots (a), (b), and (c) of Figure 12 illustrate the SDP of a M-CNN processing element, accommodating no linear resistor in the memcomputing core, under zero offset current, and for a specific value of the self-feedback synaptic weight a 0,0 in the first, second, and third of the three sets reported in Table 2 and Ascoli et al (2020b).…”

Section: Zero Offset Current Scenariomentioning

confidence: 99%

“…Let us suppose that the parameter values for b ∈ R < 0 and z ∈ R < 0 are known. As a result, TABLE 2 | Location and local stability property of each of the equilibrium points, which a M-CNN cell may possibly admit, depending upon a 0,0 , under i wi,j 0 A (Ascoli et al, 2020b). The coordinates of Q (−) , Q (0) , and Q (+) are indicated in Eqs.…”

Section: Edge M-cnnmentioning

confidence: 99%

“…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). The DRM 2 graphical tool lies at the basis of a systematic methodology to design variability-tolerant mem-computing arrays with secondorder memristive cells (Ascoli et al, 2020a).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

“…denotes an additional M-CNN cell equilibrium in the linear region (Ascoli et al, 2020b). From the first M-CNN cell ODE Eq.…”

Section: Application Of the M-cnn Design Methodology To Execute Fundamental Memcomputing Tasksmentioning

confidence: 99%

Section: Zero Offset Current Scenariomentioning

confidence: 99%

Section: Zero Offset Current Scenariomentioning

confidence: 99%

Section: Edge M-cnnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

show abstract

Theory and Technology of Memristive Devices

Tetzlaff

Ascoli

Wouters

2022

Wiley Encyclopedia of Electrical and Electronics Engineering

View full text Add to dashboard Cite

CMOS scaling is progressively and inevitably approaching atomic boundaries. The industry is thus exploring the potential of novel disruptive nanotechnologies, based on multifunctional materials, which may allow the development of integrated circuits keeping the trend predicted by Moore in 1965 in the years to come, despite further transistor shrinking being no longer possible. Memristors, originally postulated only theoretically out of a brilliant line of thought by Chua in 1971 and identified at the nanoscale almost 40 years later, back in 2008, by a team of engineers supervised by R.S. Williams at Hewlett Packard Labs, represent the key nanotechnology of the future, enabling novel forms of computation, which are closer to the principles underlying the functionalities of the human brain, given the extraordinarily peculiar capability of these devices to sense, store, and process data in the same physical miniaturized volume. Achieving progress in memristor circuit design crucially calls for the development of synergies among researchers with different academic backgrounds. In fact, only combining the technical knowledge, acquired by memristor theoreticians, with the practical know‐how of experimenters will enable to foster progress in memristor circuit and system development in the near future. In line with this necessity, the present article is the fruit of a joint cooperation between two leading memristor research units from Germany, one based at TU Dresden, which has contributed to establish solid theoretical foundations on resistance switching memories and their circuits since 2008, and the other one based at RWTH Aachen University, which has been the leading experimental research unit on nanostructures of this kind over the same time span. This article first presents a comprehensive overview of the theory of memristors, starting off from the early achievements in the pioneering studies of their father Chua, then classifies and analyses in depth the main physical mechanisms underlying the inherently nonlinear behavior of their physical realizations, and, finally, discusses their most promising applications, from the development of new nonvolatile memories based on resistance switching phenomena to the realization of novel neuromorphic circuits, capable to mimic the complex dynamics of biological entities closer than conventional purely CMOS hardware, without leaving aside an excursus on the potential to leverage the unique features of these devices for the circuit implementation of unconventional brain‐inspired time‐ and energy‐efficient sensing and memcomputing strategies, which is a great appeal for the realization of portable light‐weight technical systems for the Internet‐of‐Things industry, especially but not only to the benefit of healthcare, well‐being, and automotive market sectors.

show abstract