Solvable model of a phase oscillator network on a circle with   infinite-range Mexican-hat-type interaction
  We describe a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction. We derive self-consistent equations of the order parameters and obtain three non-trivial solutions characterized by the rotation number. We also derive relevant characteristics such as the location-dependent distributions of the resultant frequencies of desynchronized oscillators. Simulation results closely agree with the theoretical ones. 
Tatsuya Uezu, Tomoyuki Kimoto, Masato Okada
cond-mat.dis-nn cond-mat.stat-mech nlin.CD