Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

F. Caravelli, P. Barucca

Submitted to European Physical Journal B (2017)

#memristors#phasetransition#dynamicalsystems

Download the PDF

LQ placeholderIn this paper we sketch a general methodology for studying the phase diagram of memristive circuits.

In this paper we sketch a general methodology for studying the phase diagram of memristive circuits.

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 model with non-linear self-interactions. We use the Lyapunov function as an 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.

LQ placeholder

Degree-correlations in a bursting dynamic network model

F. Vanni, P. Barucca

Journal of Economic Interaction and Coordination

LQ placeholder

Scale of non-locality for a system of n particles

S. Talaganis, I. Teimouri

Sub. to Physical Review D

LQ placeholder

Changes to Gate Closure and its impact on wholesale electricity prices: The case of the UK

A. Facchini, A. Rubino, G. Caldarelli, G. Liddo

Energy Policy

LQ placeholder

How much can we influence the rate of innovation?

T. Fink, M. Reeves

Science Advances

LQ placeholder

The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

Nature Reviews Physics

LQ placeholder

PopRank: Ranking pages’ impact and users’ engagement on Facebook

A. Zaccaria, M. Vicario, W. Quattrociocchi, A. Scala, L. Pietronero

PLoS ONE

128 / 128 papers