Y. V. Pershin, V. A. Slipko, M. Di Ventra
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, and iii) independence of the dynamics voltage threshold with respect to the number of memristive elements in the network. 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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http://arxiv.org/abs/1205.0530
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