Parametrically modulated oscillator dimer: an analytic solution

R. Kawai, Katja Lindenberg and C. Van den Broeck

Physica A: Statistical Mechanics and its Applications, 2002, vol. 312, issue 1, 119-140

Abstract: A dimer consisting of two coupled oscillators undergoing periodic parametric modulations with a phase difference θ reveals a rich panorama of stability–instability boundaries as a function of the system parameters. It was recently established that the instabilities observed in such dimers with a phase difference θ=0 and with a phase difference θ=π qualitatively and even quantitatively capture a great deal of the behavior of a mean field model of coupled parametric oscillators with random phases that undergo collective parametric instabilities. These similarities were established numerically for lack of an analytic solution for the θ=π dimer. Herein we present an analytic solution for such a parametrically modulated dimer. We present the exact associated instability boundaries and thus improve on earlier ones generated by numerical simulations.

Keywords: Parametric oscillators; Periodic modulation; Resonance; Instability (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:312:y:2002:i:1:p:119-140

DOI: 10.1016/S0378-4371(02)00966-4

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