A meanfield 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 nonequilibrium dynamics and which resembles a longrange Ising Hamiltonian with nonlinear selfinteractions. We use the Lyapunov functional as a Hamiltonian to calculate, in the meanfield 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:

 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:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1481128
 Report Number(s):
 LAUR1723729
Journal ID: ISSN 12864854
 Grant/Contract Number:
 AC5206NA25396
 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 12864854
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; memristors
Citation Formats
Caravelli, Francesco, and Barucca, Paolo. A meanfield model of memristive circuit interaction. United States: N. p., 2018.
Web. doi:10.1209/02955075/122/40008.
Caravelli, Francesco, & Barucca, Paolo. A meanfield model of memristive circuit interaction. United States. doi:10.1209/02955075/122/40008.
Caravelli, Francesco, and Barucca, Paolo. Wed .
"A meanfield model of memristive circuit interaction". United States. doi:10.1209/02955075/122/40008. https://www.osti.gov/servlets/purl/1481128.
@article{osti_1481128,
title = {A meanfield 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 nonequilibrium dynamics and which resembles a longrange Ising Hamiltonian with nonlinear selfinteractions. We use the Lyapunov functional as a Hamiltonian to calculate, in the meanfield 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 = {10.1209/02955075/122/40008},
journal = {Europhysics Letters (Online)},
number = 4,
volume = 122,
place = {United States},
year = {2018},
month = {7}
}
Web of Science
Works referencing / citing this record:
Taming a nonconvex landscape with dynamical longrange order: Memcomputing Ising benchmarks
journal, November 2019
 Sheldon, Forrest; Traversa, Fabio L.; Di Ventra, Massimiliano
 Physical Review E, Vol. 100, Issue 5
Memristors for the Curious Outsiders
journal, December 2018
 Caravelli, Francesco; Carbajal, Juan
 Technologies, Vol. 6, Issue 4