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Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies f...

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Autores principales: Papadopoulos, Lia, Kim, Jason Z., Kurths, Jürgen, Bassett, Danielle S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: AIP Publishing LLC 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5552408/
https://www.ncbi.nlm.nih.gov/pubmed/28764402
http://dx.doi.org/10.1063/1.4994819
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author Papadopoulos, Lia
Kim, Jason Z.
Kurths, Jürgen
Bassett, Danielle S.
author_facet Papadopoulos, Lia
Kim, Jason Z.
Kurths, Jürgen
Bassett, Danielle S.
author_sort Papadopoulos, Lia
collection PubMed
description Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule—which preserves connections between more out-of-phase oscillators while rewiring connections between more in-phase oscillators—can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree–frequency and frequency–neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules.
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spelling pubmed-55524082017-08-29 Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators Papadopoulos, Lia Kim, Jason Z. Kurths, Jürgen Bassett, Danielle S. Chaos Regular Articles Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule—which preserves connections between more out-of-phase oscillators while rewiring connections between more in-phase oscillators—can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree–frequency and frequency–neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules. AIP Publishing LLC 2017-07 2017-07-25 /pmc/articles/PMC5552408/ /pubmed/28764402 http://dx.doi.org/10.1063/1.4994819 Text en © 2017 Author(s). 1054-1500/2017/27(7)/073115/26 All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Regular Articles
Papadopoulos, Lia
Kim, Jason Z.
Kurths, Jürgen
Bassett, Danielle S.
Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title_full Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title_fullStr Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title_full_unstemmed Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title_short Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
title_sort development of structural correlations and synchronization from adaptive rewiring in networks of kuramoto oscillators
topic Regular Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5552408/
https://www.ncbi.nlm.nih.gov/pubmed/28764402
http://dx.doi.org/10.1063/1.4994819
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