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Peron TK, Ji P, Rodrigues FA, et al. Effects of assortative mixing in the second-order Kuramoto model. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(5):052805doi: 10.1103/PhysRevE.91.052805.
Peron, T. K., Ji, P., Rodrigues, F. A., & Kurths, J. (2015). Effects of assortative mixing in the second-order Kuramoto model. Physical review. E, Statistical, nonlinear, and soft matter physics, 91(5), 052805. https://doi.org/10.1103/PhysRevE.91.052805
Peron, Thomas K Dm, et al. "Effects of assortative mixing in the second-order Kuramoto model." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 91,5 (2015): 052805. doi: https://doi.org/10.1103/PhysRevE.91.052805
Peron TK, Ji P, Rodrigues FA, Kurths J. Effects of assortative mixing in the second-order Kuramoto model. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052805. doi: 10.1103/PhysRevE.91.052805. Epub 2015 May 11. PMID: 26066210.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052805. doi: 10.1103/PhysRevE.91.052805. Epub 2015 May 11.

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

Physical review. E, Statistical, nonlinear, and soft matter physics

Thomas K Dm Peron, Peng Ji, Francisco A Rodrigues, Jürgen Kurths

Affiliations

  1. Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, São Paulo, Brazil.
  2. Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany.
  3. Department of Physics, Humboldt University, 12489 Berlin, Germany.
  4. Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil.
  5. Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.

PMID: 26066210 DOI: 10.1103/PhysRevE.91.052805

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.

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