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

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 PSN which depends on the CGLE coefficients; MAW-like stru...

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Autores principales:	Brusch, L., Torcini, A., Van Hecke, M., Zimmermann, M.G., Bär, M.
Formato:	JOUR
Materias:	Coherent structures Complex Ginzburg-Landau equation Defect chaos Phase chaos
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01672789_v160_n3-4_p127_Brusch
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01672789_v160_n3-4_p127_Brusch
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spelling	todo:paper_01672789_v160_n3-4_p127_Brusch2023-10-03T15:04:35Z Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation Brusch, L. Torcini, A. Van Hecke, M. Zimmermann, M.G. Bär, M. Coherent structures Complex Ginzburg-Landau equation Defect chaos Phase chaos 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 PSN which depends on the CGLE coefficients; MAW-like structures with period larger than PSN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients ν≈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 PSN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than PSN. In other words, MAWs with period PSN 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 PSN has diverged, phase chaos persists in the thermodynamic limit. © 2001 Published by Elsevier Science B.V. Fil:Zimmermann, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01672789_v160_n3-4_p127_Brusch
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Coherent structures Complex Ginzburg-Landau equation Defect chaos Phase chaos
spellingShingle	Coherent structures Complex Ginzburg-Landau equation Defect chaos Phase chaos Brusch, L. Torcini, A. Van Hecke, M. Zimmermann, M.G. Bär, M. Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
topic_facet	Coherent structures Complex Ginzburg-Landau equation Defect chaos Phase chaos
description	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 PSN which depends on the CGLE coefficients; MAW-like structures with period larger than PSN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients ν≈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 PSN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than PSN. In other words, MAWs with period PSN 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 PSN has diverged, phase chaos persists in the thermodynamic limit. © 2001 Published by Elsevier Science B.V.
format	JOUR
author	Brusch, L. Torcini, A. Van Hecke, M. Zimmermann, M.G. Bär, M.
author_facet	Brusch, L. Torcini, A. Van Hecke, M. Zimmermann, M.G. Bär, M.
author_sort	Brusch, L.
title	Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
title_short	Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
title_full	Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
title_fullStr	Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
title_full_unstemmed	Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
title_sort	modulated amplitude waves and defect formation in the one-dimensional complex ginzburg-landau equation
url	http://hdl.handle.net/20.500.12110/paper_01672789_v160_n3-4_p127_Brusch
work_keys_str_mv	AT bruschl modulatedamplitudewavesanddefectformationintheonedimensionalcomplexginzburglandauequation AT torcinia modulatedamplitudewavesanddefectformationintheonedimensionalcomplexginzburglandauequation AT vanheckem modulatedamplitudewavesanddefectformationintheonedimensionalcomplexginzburglandauequation AT zimmermannmg modulatedamplitudewavesanddefectformationintheonedimensionalcomplexginzburglandauequation AT barm modulatedamplitudewavesanddefectformationintheonedimensionalcomplexginzburglandauequation
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Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

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