title: Continuous and discontinuous transitions to synchronization.
abstract: We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the latter is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exists at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Chaoqing
authors.initials: C
authors.lastname: Wang
authors.affiliation: Laboratoire de Physique, Univ. Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, F-69342 Lyon, France.
authors.forename: Nicolas B
authors.initials: NB
authors.lastname: Garnier