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Critical Behaviors in Contagion Dynamics

L. Böttcher, J. Nagler, and H. J. Herrmann
Phys. Rev. Lett. 118, 088301 – Published 23 February 2017
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Abstract

We study the critical behavior of a general contagion model where nodes are either active (e.g., with opinion A, or functioning) or inactive (e.g., with opinion B, or damaged). The transitions between these two states are determined by (i) spontaneous transitions independent of the neighborhood, (ii) transitions induced by neighboring nodes, and (iii) spontaneous reverse transitions. The resulting dynamics is extremely rich including limit cycles and random phase switching. We derive a unifying mean-field theory. Specifically, we analytically show that the critical behavior of systems whose dynamics is governed by processes (i)–(iii) can only exhibit three distinct regimes: (a) uncorrelated spontaneous transition dynamics, (b) contact process dynamics, and (c) cusp catastrophes. This ends a long-standing debate on the universality classes of complex contagion dynamics in mean field and substantially deepens its mathematical understanding.

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  • Received 9 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.088301

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary PhysicsNetworksStatistical Physics & Thermodynamics

Authors & Affiliations

L. Böttcher*, J. Nagler, and H. J. Herrmann

  • ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland

  • *lucasb@ethz.ch
  • jnagler@ethz.ch

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Issue

Vol. 118, Iss. 8 — 24 February 2017

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