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

TL;DR

This paper investigates the chaotic dynamics of holes and defects in the 1D complex Ginzburg-Landau equation, highlighting the role of self-disordering backgrounds in driving spatiotemporal chaos.

Contribution

It introduces a lattice model that captures the essential chaotic behavior of the 1D CGLE by focusing on self-disordering effects.

Findings

Coupling to a self-disordered background is the main chaos driver.

A simplified lattice model reproduces key chaotic features.

Self-disordering dynamics are crucial for understanding defect chaos.

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.