Transition from Torus to Chaos Accompanied by Frequency Lockings with Symmetry Breaking: In Connection with the Coupled-Logistic Map

Transition from torus to chaos is studied using the coupled-logistic map. We observe the period-adding sequence, which obeys the critical phenomena of a one-dimensional mapping. The fixed Lyapunov exponent is also obtained. The locking that appears after the sequence breaks the symmetry of the system. Self-similar stripe structure of basins is also found. Various properties and a phase diagram of the map are given. The mechanism of the distortion of torus and transition to chaos is also discussed.