Locality of interactions for planar memristive circuits

F. Caravelli
Phys. Rev. E 96, 052206 – Published 8 November 2017

Abstract

The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for which a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. This result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.

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  • Received 9 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.052206

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

F. Caravelli

  • Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 96, Iss. 5 — November 2017

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