ARNOL’D TONGUES, DEVIL’S STAIRCASE, AND SELF-SIMILARITY IN THE DRIVEN CHUA’S CIRCUIT

Abstract

Empirical recurrent relations, governing the structure of the devil’s staircase in the driven Chua’s circuit are given, which reflect the self-similar structure in an algebraic form. In particular, it turns out that the same formulas hold for both winding and period numbers, but with different “initial conditions”. Some of the finer details such as period-doubling along with numerous coexistence phenomena within staircases of mode-locked states have been revealed by computing high-resolution bifurcation diagrams.