Fractalization of a torus and its transition to chaos in a quasiperiodically forced logistic map is reinvestigated in relation to a strange nonchaotic attractor, with the aid of a functional equation for the invariant curve. The existence of a fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of a fractal torus and the transition to chaos are studied in connection with the intermittency.

• Received 1 July 1996

DOI:https://doi.org/10.1103/PhysRevE.54.6114