Circle maps and mode locking in the driven electrical conductivity of barium sodium niobate crystals

Instabilities in the electrical conductivity of barium sodium niobate crystals are studied with ac and dc fields. Phase portraits, Poincaré sections, and return maps are constructed from measured signals in the quasiperiodic state. We show that the dynamical behavior of the system can be modeled by a 1D circle map. Mode locking is observed in the system prior to the transition to chaos; the mode-locked intervals exhibit a Devil's staircase behavior.