Phase-Induced (In)-Stability in Coupled Parametric Oscillators

Abstract

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $\theta$. Being to a large extent analytically solvable, the model reveals a rich $\theta$ 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.

19 pages, 8 figures; a version with better quality figures can be found in http://hypatia.ucsd.edu/~mauro/English/publications.html

References in corpus (2)

• Remarks on parametric resonance of neutrino oscillations in the earth
• Heisenberg picture approach to the invariants and the exact quantum motions for coupled parametric oscillators

Cited by in corpus (2)

• On the Collective Behavior of Parametric Oscillators
• Detecting the $\pi$-axiverse through parametric resonance