Escaping the avalanche collapse in self-similar multiplexes

M. Angeles Serrano; Lubos Buzna; Marian Boguna

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arXiv · 1502.04553

Escaping the avalanche collapse in self-similar multiplexes

M. Angeles Serrano·Lubos Buzna·Marian Boguna

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Abstract

We deduce and discuss the implications of self-similarity for the stability in terms of robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the stability properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary stability attributes of noninteracting networks. We confirm these results with numerical simulations.

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M. Angeles Serrano, Lubos Buzna, Marian Boguna. 2015-02-16. Escaping the avalanche collapse in self-similar multiplexes. https://arxiv.org/abs/1502.04553

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