title: Effects of degree correlations on the explosive synchronization of scale-free networks.
abstract: We study the organization of finite-size, large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are known to occur in growing scale-free networks, while the transition has a completely different nature for static random configurations preserving the same structure-dynamics correlation. We show that the further presence of degree-degree correlations in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in scale-free networks. The latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.
authors: Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors: I
authors: I
authors: Sendiña-Nadal
authors: Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors: I
authors: I
authors: Leyva
authors: Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors: A
authors: A
authors: Navas
authors: Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors: J A
authors: JA
authors: Villacorta-Atienza
authors: Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors: J A
authors: JA
authors: Almendral
authors: Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China.|Center for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong) and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China.
authors: Z
authors: Z
authors: Wang
authors: CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.|Italian Embassy in Israel, 25 Hamered Street, 68125 Tel Aviv, Israel.
authors: S
authors: S
authors: Boccaletti
mesh_terms: D008962:Models, Theoretical