Torus window in a torus‐doubling generating circuit

Abstract

AbstractAn extremely significant transition phenomenon from a periodic phase to a chaotic phase is known as torus doubling. In this research, we perform computer simulations to study what kind of periodic behavior exists in the chaotic phase transitioned into due to torus doubling in an electrical circuit that generates torus doubling. The result was the generation of an n‐fold torus that is believed to be deeply related to the period of a relatively large window that appears in the chaotic phase in logistic maps such as a 6‐fold, 5‐fold, or 3‐fold torus in the chaotic phase. In this paper, we call the torus generated in the gap of this chaotic phase the torus window. We also analyze a coupled model consisting of a logistic map and a sine‐circle map as the model to explain the mechanism for generating the torus window. We perform computer simulations to show that the 6‐, 5‐, and 3‐fold torus windows are generated in this model. © 2002 Scripta Technica, Electron Comm Jpn Pt 3, 85(5): 56–62, 2002