A mean-field model of memristive circuit interaction

Caravelli, Francesco; Barucca, Paolo

doi:10.1209/0295-5075/122/40008

Title: A mean-field model of memristive circuit interaction

Abstract

We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact fixed points can be obtained. Here, we introduce a Lyapunov functional that is found to be minimized along the non-equilibrium dynamics and which resembles a long-range Ising Hamiltonian with non-linear self-interactions. We use the Lyapunov functional as a Hamiltonian to calculate, in the mean-field theory approximation, the average asymptotic behavior of the circuit given a random initialization, yielding exact predictions for the case of decay to the lower resistance state, and reasonable predictions for the case of a decay to the higher resistance state.

Authors:

^[1]; Barucca, Paolo ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. College London, London (United Kingdom). Dept. of Computer Science; London Inst. for Mathematical Sciences, London (United Kingdom)

Publication Date:: Wed Jul 04 00:00:00 EDT 2018

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1481128

Report Number(s):: LA-UR-17-23729
Journal ID: ISSN 1286-4854

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Europhysics Letters (Online)

Additional Journal Information:: Journal Name: Europhysics Letters (Online); Journal Volume: 122; Journal Issue: 4; Journal ID: ISSN 1286-4854

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; memristors

Citation Formats


                    Caravelli, Francesco, and Barucca, Paolo. A mean-field model of memristive circuit interaction.  United States: N. p., 2018. 
Web.  doi:10.1209/0295-5075/122/40008.

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                    Caravelli, Francesco, & Barucca, Paolo. A mean-field model of memristive circuit interaction.  United States.  https://doi.org/10.1209/0295-5075/122/40008

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                    Caravelli, Francesco, and Barucca, Paolo. Wed .  
"A mean-field model of memristive circuit interaction".  United States.  https://doi.org/10.1209/0295-5075/122/40008.  https://www.osti.gov/servlets/purl/1481128.

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@article{osti_1481128,

  title        = {A mean-field model of memristive circuit interaction},

  author       = {Caravelli, Francesco and Barucca, Paolo},

  abstractNote = {We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact fixed points can be obtained. Here, we introduce a Lyapunov functional that is found to be minimized along the non-equilibrium dynamics and which resembles a long-range Ising Hamiltonian with non-linear self-interactions. We use the Lyapunov functional as a Hamiltonian to calculate, in the mean-field theory approximation, the average asymptotic behavior of the circuit given a random initialization, yielding exact predictions for the case of decay to the lower resistance state, and reasonable predictions for the case of a decay to the higher resistance state.},

  doi          = {10.1209/0295-5075/122/40008},

  journal      = {Europhysics Letters (Online)},

  number       = 4,

  volume       = 122,

  place        = {United States},

  year         = {Wed Jul 04 00:00:00 EDT 2018},

  month        = {Wed Jul 04 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

Taming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks
journal, November 2019

Sheldon, Forrest; Traversa, Fabio L.; Di Ventra, Massimiliano
Physical Review E, Vol. 100, Issue 5
DOI: 10.1103/physreve.100.053311

Memristors for the Curious Outsiders
journal, December 2018

Caravelli, Francesco; Carbajal, Juan
Technologies, Vol. 6, Issue 4
DOI: 10.3390/technologies6040118

Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
text, January 2018

Sheldon, Forrest; Traversa, Fabio L.; Di Ventra, Massimiliano
arXiv
DOI: 10.48550/arxiv.1810.03712

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Similar Records

Title: A mean-field model of memristive circuit interaction

Abstract

Citation Formats

Taming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks journal, November 2019

Memristors for the Curious Outsiders journal, December 2018

Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks text, January 2018

Taming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks
journal, November 2019

Memristors for the Curious Outsiders
journal, December 2018

Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
text, January 2018