Stability of synchronization in dissipatively driven Frenkel-Kontorova   models
  We rigorously show that dissipatively driven Frenkel-Kontorova models with either uniform or time-periodic driving asymptotically synchronize for a wide range of initial conditions. The main tool is a new Lyapunov function, as well as a 2D representation of the attractor. We then characterize dynamical phase transitions and outline new algorithms for determining them. 
Sinisa Slijepcevic
math.DS math-ph math.MP