title: Analysis of cluster explosive synchronization in complex networks.
abstract: Correlations between intrinsic dynamics and local topology have become a new trend in the study of synchronization in complex networks. In this paper, we investigate the influence of topology on the dynamics of networks made up of second-order Kuramoto oscillators. In particular, based on mean-field calculations, we provide a detailed investigation of cluster explosive synchronization (CES) [Phys. Rev. Lett. 110, 218701 (2013)] in scale-free networks as a function of several topological properties. Moreover, we investigate the robustness of discontinuous transitions by including an additional quenched disorder, and we show that the phase coherence decreases with increasing strength of the quenched disorder. These results complement the previous findings regarding CES and also fundamentally deepen the understanding of the interplay between topology and dynamics under the constraint of correlating natural frequencies and local structure.
authors.affiliation: Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Department of Physics, Humboldt University, 12489 Berlin, Germany.
authors.forename: Peng
authors.initials: P
authors.lastname: Ji
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil.
authors.forename: Thomas K D M
authors.initials: TK
authors.lastname: Peron
authors.affiliation: 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.
authors.forename: Francisco A
authors.initials: FA
authors.lastname: Rodrigues
authors.affiliation: Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Department of Physics, Humboldt University, 12489 Berlin, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths