We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference θ. Being to a large extent analytically solvable, the model reveals a rich θ dependence of the regions of parametric resonance. In particular, the intuitive notion that antiphase modulations are less prone to parametric resonance is confirmed for sufficiently large coupling and damping. Some general results concerning synchronization properties in this system are presented. We also compare our results to a recently reported mean-field model of collective parametric instability, showing that the two-oscillator model captures much of the qualitative behavior of the infinite system.

• Received 1 August 2000

DOI:https://doi.org/10.1103/PhysRevE.63.036605