Contraction of monotone phase-coupled oscillators
  This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state. 
Alexandre Mauroy and Rodolphe Sepulchre
math.DS