Exactly solvable phase oscillator models with synchronization dynamics
  Populations of phase oscillators interacting globally through a general coupling function $f(x)$ have been considered. In the absence of precessing frequencies and for odd-coupling functions there exists a Lyapunov functional and the probability density evolves toward stable stationary states described by an equilibrium measure. We have then proposed a family of exactly solvable models with singular couplings which synchronize more easily as the coupling becomes less singular. The stationary solutions of the least singular coupling considered, $f(x)=$ sign$(x)$, have been found analytically in terms of elliptic functions. This last case is one of the few non trivial models for synchronization dynamics which can be analytically solved. 
L. L. Bonilla, C. Perez-Vicente, F. Ritort and J. Soler