Complex dynamics and scale invariance of one-dimensional memristive networks

TL;DR

This paper investigates the complex dynamics and scale invariance in one-dimensional memristive networks, revealing how variability and memory effects influence their physical behavior and potential technological applications.

Contribution

It demonstrates novel physical properties of simple memristive networks, including scale invariance and avalanche phenomena, considering element variability and input history effects.

Findings

Dynamical acceleration and slowing down in resistance during adiabatic processes

Final state dependence on input signal history

Existence of switching avalanches in memristive ladders

Abstract

Memristive systems, namely resistive systems with memory, are attracting considerable attention due to their ubiquity in several phenomena and technological applications. Here, we show that even the simplest one-dimensional network formed by the most common memristive elements with voltage threshold bears non-trivial physical properties. In particular, by taking into account the single element variability we find i) dynamical acceleration and slowing down of the total resistance in adiabatic processes, ii) dependence of the final state on the history of the input signal with same initial conditions, iii) existence of switching avalanches in memristive ladders, and iv) 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.