Bifurcational mechanisms of synchronization of a resonant limit cycle on a two-dimensional torus

We study synchronization of a resonant limit cycle on a two-dimensional torus with an external harmonic signal. The regime of the resonant limit cycle is realized in a system of two coupled Van der Pol oscillators; we consider the resonances 1:1 and 1:3. We analyze the influence of coupling strength between the oscillators. We show that the resonant limit cycle can be generally synchronized on the torus through the resonance destruction followed by the locking of one and then another one of the basic frequencies. We consider the bifurcational mechanism of the synchronization effect. (C) 2008 American Institute of Physics.