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Maintaining extensivity in evolutionary multiplex networks

Antonopoulos, CG and Baptista, MS (2017) 'Maintaining extensivity in evolutionary multiplex networks.' PLoS ONE, 12 (4). ISSN 1932-6203

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Abstract

© 2017 Antonopoulos, Baptista. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, HKS, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size N, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as Nθ+1, θ > 0, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as N-θ, when evolution is driven by the maximisation of HKS. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Chris Antonopoulos
Date Deposited: 19 Apr 2017 10:25
Last Modified: 26 Jun 2018 10:15
URI: http://repository.essex.ac.uk/id/eprint/19467

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