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

Lia Papadopoulos, Jason Kim, Jurgen Kurths, Danielle S. Bassett

Research output: Contribution to journalArticle

8 Citations (Scopus)
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Abstract

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several studies have uncovered optimal topologies for synchronization by making purposeful alterations to a network. Yet, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. This co-evolution - and the extent to which the dynamics of the individual units can shape the organization of the network itself - is not well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. The system employs a co-evolutionary rewiring strategy that depends only on 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 regulatory 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 both a dependence on the intrinsic frequencies of the oscillators and the global coupling. For large enough coupling and after sufficient adaptation, the resulting networks exhibit degree - frequency and frequency - neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions. By considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena can arise in complex systems utilizing local rules.
Original languageEnglish
Article number073115
Number of pages31
JournalChaos
Volume27
Issue number7
DOIs
Publication statusPublished - Jul 2017

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synchronism
Synchronization
oscillators
Topology
Complex networks
topology
Large scale systems
Evolutionary Strategy
Locally Connected
Collective Behavior
Coevolution
Phase Difference
Conserve
Coupled Oscillators
Complex Networks
Instantaneous
complex systems
Pairwise
Complex Systems
Connectivity

Keywords

  • oscillators
  • topology
  • wave mechanics
  • neuronal network dynamics
  • complex systems

Cite this

Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators. / Papadopoulos, Lia; Kim, Jason; Kurths, Jurgen; Bassett, Danielle S.

In: Chaos, Vol. 27, No. 7, 073115 , 07.2017.

Research output: Contribution to journalArticle

Papadopoulos, Lia ; Kim, Jason ; Kurths, Jurgen ; Bassett, Danielle S. / Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators. In: Chaos. 2017 ; Vol. 27, No. 7.
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abstract = "Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several studies have uncovered optimal topologies for synchronization by making purposeful alterations to a network. Yet, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. This co-evolution - and the extent to which the dynamics of the individual units can shape the organization of the network itself - is not well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. The system employs a co-evolutionary rewiring strategy that depends only on 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 regulatory 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 both a dependence on the intrinsic frequencies of the oscillators and the global coupling. For large enough coupling and after sufficient adaptation, the resulting networks exhibit degree - frequency and frequency - neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions. By considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena can arise in complex systems utilizing local rules.",
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note = "L.P. acknowledges support from the National Science Foundation Graduate Research Fellowship Program. J.K. acknowledges support from the National Science Foundation Graduate Research Fellowship Program and NIH T32-EB020087, PD: Felix W. Wehrli. D.S.B. also acknowledges support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, and the National Science Foundation (BCS-1441502, CAREER PHY-1554488, BCS-1631550, and CNS-1626008). We also thank two anonymous reviewers whose comments greatly improved the quality of this work. The content is solely the responsibility of the authors and does not necessarily represent the official views of any of the funding agencies.",
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