Pendulum limit, chaos and phase-locking in the dynamics of ac-driven   semiconductor superlattices
  We describe a limiting case when nonlinear dynamics of an ac-driven semiconductor superlattice in the miniband transport regime is governed by a periodically forced and damped pendulum. We find analytically the conditions for a transition to chaos and consider an influence of temperature on the effect. We also discuss fractional dc voltage states in a superlattice originating from phase-locked states of the pendulum. 
Kirill N. Alekseev and Feodor V. Kusmartsev