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Mobility induces global synchronization of oscillators in periodic extended systems

Peruani, Fernando; Nicola, Ernesto M.; Morelli, Luis G.
New Journal of Physics 12, 093029 (2010)

We study the synchronization of locally coupled noisy phase oscillators that move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits wave-like states displaying local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical mobility above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by a shift in the relative size of attractor basins associated with wave-like states. Mobility disrupts these states and paves the way for the system to attain global synchronization.