Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • L Brusch - , Max-Planck-Institute for the Physics of Complex Systems (Author)
  • A Torcini - (Author)
  • M van Hecke - (Author)
  • MG Zimmermann - (Author)
  • M Bar - (Author)

Abstract

The transition from phase chaos to defect chaos in the complex Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown to be limited by a maximum P-SN which depends on the CGLE coefficients; MAW-like structures with period larger than P-SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients v approximate to 0 and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings p between neighbouring peaks of the phase gradient. A systematic comparison of p and P-SN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than P-SN. In other words, MAWs with period P-SN represent "critical nuclei" for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time, We conjecture that in the regime where the maximum period P-SN has diverged, phase chaos persists in the thermodynamic limit. (C) 2001 Published by Elsevier Science B.V.

Details

Original languageEnglish
Pages (from-to)127-148
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume160
Issue number3-4
Publication statusPublished - 15 Dec 2001
Peer-reviewedYes
Externally publishedYes

External IDs

Scopus 0035892848
ORCID /0000-0003-0137-5106/work/142244224

Keywords

Keywords

  • phase chaos, defect chaos, complex Ginzburg-Landau equations, coherent structures, PHASE-TURBULENCE, SPATIOTEMPORAL CHAOS, ECKHAUS INSTABILITY, TRANSITION, DYNAMICS, DRIVEN, FRONTS, PULSES, INTERMITTENCY, PROPAGATION