Phase and amplitude dynamics of nonlinearly coupled oscillators

Chaos
P Cudmore, C A Holmes

Abstract

This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.

References

Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M C CrossA Zumdieck
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C A HolmesG J Milburn

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Citations

Dec 15, 2021·The European Physical Journal. E, Soft Matter·Peter CudmoreEdmund J Crampin

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