Response of discrete nonlinear systems with many degrees of freedom.

@article{Bromberg2006ResponseOD,
  title={Response of discrete nonlinear systems with many degrees of freedom.},
  author={Yaron Bromberg and Michael C. Cross and Ron Lifshitz},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2006},
  volume={73 1 Pt 2},
  pages={
          016214
        }
}
We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wave-number… 

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