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Complex dynamics and scale invariance of one-dimensional memristive networks

Yuriy V. Pershin1,*, Valeriy A. Slipko2,†, and Massimiliano Di Ventra3,‡

  • 1Department of Physics and Astronomy and University of South Carolina Nanocenter, University of South Carolina, Columbia, South Carolina 29208, USA
  • 2Department of Physics and Technology, V. N. Karazin Kharkov National University, Kharkov 61077, Ukraine
  • 3Department of Physics, University of California, San Diego, California 92093-0319, USA

  • *pershin@physics.sc.edu
  • †slipko@univer.kharkov.ua
  • ‡diventra@physics.ucsd.edu
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Phys. Rev. E 87, 022116 – Published 14 February, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.022116

Abstract

Memristive systems, namely, resistive systems with memory, are currently attracting considerable attention. Here we show that even the simplest one-dimensional network formed by the most common memristive elements with voltage threshold bears nontrivial physical properties. In particular, by taking into account the single element variability we find (1) dynamical acceleration and slowing down of the total resistance in adiabatic processes, (2) dependence of the final state on the history of the input signal with same initial conditions, (3) existence of switching avalanches in memristive ladders, and (4) independence of the dynamics voltage threshold with respect to the number of memristive elements in the network (scale invariance). An important criterion for this scale invariance is the presence of memristive systems with very small threshold voltages in the ensemble. These results elucidate the role of memory in complex networks and are relevant to technological applications of these systems.

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Phys. Rev. E 87, 022116– Published 14 February, 2013
  • Received 2 May 2012
Article part of CHORUS

©2013 American Physical Society

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