Winding number locking on a two-dimensional torus: synchronization of quasiperiodic motions.
We propose a new autonomous dynamical system of dimension N = 4 that demonstrates the regime of stable two-frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two-dimensional torus takes place.
Anishchenko
V
V
Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, Russia. wadim@chaos.ssu.runnet.ru
Nikolaev
S
S
Kurths
J
J