Loss of coherence among coupled oscillators: From defect states to phase turbulence.

Synchronization of a large ensemble of identical phase oscillators with a nonlocal kernel and a phase lag parameter α is investigated for the classical Kuramoto-Sakaguchi model on a ring. We demonstrate, for low enough coupling radius r and α below π/2, a phase transition between coherence and phase turbulence via so-called defect states, which arise at the early stage of the transition. The defect states are a novel object resulting from the concatenation of two or more uniformly twisted waves with different wavenumbers. Upon further increase of α, defects lose their stability and give rise to spatiotemporal intermittency, resulting eventually in developed phase turbulence. Simulations close to the thermodynamic limit indicate that this phase transition is characterized by nonuniversal critical exponents.