Effects of assortative mixing in the second-order Kuramoto model

Thomas K. D. M. Peron*, Peng Ji, Francisco A. Rodrigues, Jurgen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticle

20 Citations (Scopus)
3 Downloads (Pure)

Abstract

In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.

Original languageEnglish
Article number052805
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume91
Issue number5
DOIs
Publication statusPublished - 11 May 2015

Keywords

  • scale-free networks
  • complex networks
  • phase oscillators
  • synchronization
  • stability
  • transition
  • paradign
  • inertia

Cite this

Effects of assortative mixing in the second-order Kuramoto model. / Peron, Thomas K. D. M.; Ji, Peng; Rodrigues, Francisco A.; Kurths, Jurgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 5, 052805, 11.05.2015.

Research output: Contribution to journalArticle

Peron, Thomas K. D. M. ; Ji, Peng ; Rodrigues, Francisco A. ; Kurths, Jurgen. / Effects of assortative mixing in the second-order Kuramoto model. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2015 ; Vol. 91, No. 5.
@article{14430c5f8d4f44b4a7cb31b44f59d2a8,
title = "Effects of assortative mixing in the second-order Kuramoto model",
abstract = "In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.",
keywords = "scale-free networks, complex networks, phase oscillators, synchronization, stability, transition, paradign, inertia",
author = "Peron, {Thomas K. D. M.} and Peng Ji and Rodrigues, {Francisco A.} and Jurgen Kurths",
note = "ACKNOWLEDGMENTS T.P. would like to acknowledge FAPESP (No. 2012/22160-7) and IRTG 1740. P.J. would like to acknowledge China Scholarship Council (CSC) scholarship. F.A.R. would like to acknowledge CNPq (No. 305940/2010-4), FAPESP (No. 2010/19440- 2), and IRTG 1740 for the financial support given to this research. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP) for the sponsorship provided.",
year = "2015",
month = "5",
day = "11",
doi = "10.1103/PhysRevE.91.052805",
language = "English",
volume = "91",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "5",

}

TY - JOUR

T1 - Effects of assortative mixing in the second-order Kuramoto model

AU - Peron, Thomas K. D. M.

AU - Ji, Peng

AU - Rodrigues, Francisco A.

AU - Kurths, Jurgen

N1 - ACKNOWLEDGMENTS T.P. would like to acknowledge FAPESP (No. 2012/22160-7) and IRTG 1740. P.J. would like to acknowledge China Scholarship Council (CSC) scholarship. F.A.R. would like to acknowledge CNPq (No. 305940/2010-4), FAPESP (No. 2010/19440- 2), and IRTG 1740 for the financial support given to this research. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP) for the sponsorship provided.

PY - 2015/5/11

Y1 - 2015/5/11

N2 - In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.

AB - In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.

KW - scale-free networks

KW - complex networks

KW - phase oscillators

KW - synchronization

KW - stability

KW - transition

KW - paradign

KW - inertia

U2 - 10.1103/PhysRevE.91.052805

DO - 10.1103/PhysRevE.91.052805

M3 - Article

VL - 91

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 052805

ER -