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
anti-phase modulations are less prone to parametric resonance is confirmed for
sufficiently large coupling and damping. We also compare our results to a
recently reported mean field model of collective parametric instability,
showing that the two-oscillator model can capture much of the qualitative
behavior of the infinite system.Comment: 19 pages, 8 figures; a version with better quality figures can be
found in http://hypatia.ucsd.edu/~mauro/English/publications.htm