On the Collective Behavior of Parametric Oscillators

Details On the Collective Behavior of Parametric Oscillators On the Collective Behavior of Parametric Oscillators

2001-02-06

arxiv.org/abs/cond-mat/0102113v1

Phys. Rev. E Vol. 65, 036611 (2002)

Physics

Condensed Matter

Statistical Mechanics

17 figures, including color figures. A version of the paper with better quality figures (but much larger files) can be obtaine

Scientific paper

10.1103/PhysRevE.65.036611

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. {\bf 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, to appear in Phys. Rev. E].

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