Peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus.

The peculiarities of external synchronization of a resonant limit cycle on a torus are studied in an autonomous oscillator of quasiperiodic oscillations with two basic frequencies. We show numerically and experimentally that in the resonance conditions the synchronization effect takes place only at one of the two basic frequencies of the system, while the oscillations at the second basic frequency remain unsynchronized. Our results convincingly indicate a principal difference between synchronization of the resonant limit cycle on the torus and of a typical limit cycle. This is in contrast to the well-established theory of synchronization of a limit cycle. This finding opens new strategies for controlling systems with multiple time scales.