Successive torus doubling

In this paper, we analyze circuits which exhibit a torus doubling route to chaos. Though some researchers insisted that torus doubling occurs a finite number of times, we show that the successive occurrence of a certain kind of torus doubling, which we call "swollen shape type bifurcation," is obser ved in a certain region. This phenomenon has a very delicate structure, and when observed in a laboratory experiment is very interesting. In addition, a coupled system of a logistic map and a sin circle map is proposed as the simplest model which can explain the mechanism of the swollen shape type b ifurcation. Also, the swollen shape type bifurcation is also observed in th is system.