  We study the onset of synchronization in lattices of limit cycle oscillators
with long-range coupling by means of numerical simulations. In this regime the
critical coupling strength depends on the system size and interaction range
reflecting the non extensive behavior of the system, but an adequate scaling
removes the dependency and collapses the long-range synchronization curves with
the one resulting from a system with uniform coupling. Two descriptions are
considered, the Kuramoto or phase description model and a Cell Dynamical System
model for phases and amplitudes. Oscillator death is observed in the second
approach.
