Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation

Abstract

We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing identical defect profiles and/or smooth plane wave backgrounds, we are able to sensitively probe the causes of the spatiotemporal chaos. We show that the coupling of the holes to a self--disordered background is the dominant mechanism. We analyze a lattice model for the 1D CGLE, incorporating this self--disordering. Despite its simplicity, we show that the model retains the essential spatiotemporally chaotic behavior of the full CGLE.

8 pages, 10 figures; revised and shortened; extra discussion of self-disordering dynamics

References in corpus (4)

• The World of the Complex Ginzburg-Landau Equation
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions
• Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation