A mean-field model of memristive circuit interaction

¹ Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory Los Alamos, NM 87545, USA
² Department of Computer Science, University College London - Gower Street, London WC1E 6BT, UK
³ London Institute for Mathematical Sciences - 35a South Street, London W1K 2XF, UK

^(a) caravelli@lanl.gov

Received: 19 March 2018
Accepted: 9 June 2018

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.