title: Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations.
abstract: An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, Av. Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970, São Carlos, São Paulo, Brazil.
authors.forename: Thomas Kauê Dal'maso
authors.initials: TK
authors.lastname: Peron
authors.forename: Francisco A
authors.initials: FA
authors.lastname: Rodrigues
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*