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A mean-field model of memristive circuit interaction

Caravelli, F; Barucca, P; (2018) A mean-field model of memristive circuit interaction. EPL , 122 (4) , Article 40008. 10.1209/0295-5075/122/40008. Green open access

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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. 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.

Type: Article
Title: A mean-field model of memristive circuit interaction
Open access status: An open access version is available from UCL Discovery
DOI: 10.1209/0295-5075/122/40008
Publisher version: http://dx.doi.org/10.1209/0295-5075/122/40008
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, SYSTEMS, DEVICES
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10057190
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