Complex dynamics and scale invariance of one-dimensional memristive networks

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.

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• Metastable Memristive Lines for Signal Transmission and Information Processing Applications
• Switching Synchronization in One-Dimensional Memristive Networks
• EGaIn tube memristors offer reliable switching on a biological time scale
• Switching synchronization in 1-D memristive networks: An exact solution