PMID: 11909289Mar 23, 2002Paper

Collective behavior of parametric oscillators

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
I BenaKatja Lindenberg

Abstract

We revisit the mean-field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is a detailed characterization of the motions underlying these instabilities. This presentation includes regimes not identified in earlier work [I. Bena and C. Van den Broeck, Europhys. Lett. 48, 498 (1999)]. In addition to the familiar parametric instability of individual oscillators, two kinds of collective instabilities are identified. In one the mean amplitude diverges monotonically while in the other the divergence is oscillatory. The frequencies of collective oscillatory instabilities in general bear no simple relation to the eigenfrequencies of the individual oscillators nor to the frequency of the external modulation. Numerical simulations show that systems with only nearest-neighbor coupling have collective instabilities similar to those of the mean-field model. Many of the mean-field results are already apparent in a simple dimer [M. Copelli and K. Lindenberg, Phys. Rev. E 63, 036605 (2001)].

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Citations

Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Romi MankinEerik Reiter
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Erkki SoikaAin Ainsaar
Mar 24, 2005·Physical Review Letters·F PétrélisS Fauve
May 21, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Romi Mankin, Astrid Rekker

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