Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator

We report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped-driven Duffing oscillator as the amplitude of the drive increases. Families of period-adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force grows. Such surprising regularities suggest that some hitherto unknown renormalization mechanism may be operating in higher codimension, controlling the alternation of chaos and order in parameter space of certain flows.