Synchronization in large populations of limit cycle oscillators with long-range interactions

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.