Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions

Details Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions

2002-03-09

arxiv.org/abs/cond-mat/0203206v1

Phys. Rev. E Vol.65, 046208 (2002)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures, 2 column revtex format, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.65.046208

In this paper we study the effect of external harmonic forcing on a one-dimensional oscillatory system described by the complex Ginzburg-Landau equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous state with no spatial structure is observed. The state becomes unstable to a spatially periodic ``stripe'' state via a supercritical bifurcation as the forcing amplitude decreases. An approximate phase equation is derived, and an analytic solution for the stripe state is obtained, through which the asymmetric behavior of the stability border of the state is explained. The phase equation, in particular the analytic solution, is found to be very useful in understanding the stability borders of the homogeneous and stripe states of the forced CGLE.

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