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Symmetric States Requiring System Asymmetry

Takashi Nishikawa and Adilson E. Motter
Phys. Rev. Lett. 117, 114101 – Published 7 September 2016; Erratum Phys. Rev. Lett. 117, 189902 (2016)
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Abstract

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking—the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.

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  • Received 27 May 2016
  • Publisher error corrected 10 October 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.114101

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsNetworks

Corrections

10 October 2016

Erratum

Publisher’s Note: Symmetric States Requiring System Asymmetry [Phys. Rev. Lett. 117, 114101 (2016)]

Takashi Nishikawa and Adilson E. Motter
Phys. Rev. Lett. 117, 189902 (2016)

Synopsis

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Diversity Breeds Conformity

Published 7 September 2016

Coupled oscillators in certain networks will—counterintuitively—only move in tandem if each oscillator is different.

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Authors & Affiliations

Takashi Nishikawa* and Adilson E. Motter

  • Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA and Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA

  • *Corresponding author. t-nishikawa@northwestern.edu

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Issue

Vol. 117, Iss. 11 — 9 September 2016

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