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Updated: Aug 7, 2026

Magnetic Tweezers for the Measurement of Twist and Torque
Published on: May 19, 2014
Winding number locking on a two-dimensional torus: synchronization of quasiperiodic motions
V Anishchenko1, S Nikolaev, J Kurths
1Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, Russia. wadim@chaos.ssu.runnet.ru
Abstract:
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.
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