Fractalization of a torus as a strange nonchaotic attractor

1996/12/01 by Takashi Nishikawa, Kunihiko Kaneko · 2 citations
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.1103/physreve.54.6114

openalex publication_date 1996/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

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.

Cited by

• Mechanism for the intermittent route to strange nonchaotic attractors
• Weird quasiperiodic attractors and strange nonchaotic attractors in two-dimensional discontinuous maps

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