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.
Documento: | Artículo |
Título: | Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation |
Autor: | Brusch, L.; Torcini, A.; Van Hecke, M.; Zimmermann, M.G.; Bär, M. |
Filiación: | Max-Planck-Institut für Physik Komplexer Systeme, Nothnitzer Strae 38, D-01187 Dresden, Germany Dipartimento di Fisica, Università la Sapienza, P.le A. Moro 2, I-00185 Rome, Italy Istituto Nazionale di Fisica della Materia, Unità di Firenze, Largo Enrico Fermi 2, I-50125 Firenze, Italy Center for Chaos and Turbulence Studies, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark Kamerlingh Onnes Laboratory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, Netherlands Instituto Mediterráneo de Estudios Avanzados, IMEDEA (CSIC-UIB), E-07071 Palma de Mallorca, Spain Departamento de Física, FCEN-Universidad de Buenos Aires, Pab. i Ciudad Universitaria, 1428 Buenos Aires, Argentina |
Palabras clave: | Coherent structures; Complex Ginzburg-Landau equation; Defect chaos; Phase chaos |
Año: | 2001 |
Volumen: | 160 |
Número: | 3-4 |
Página de inicio: | 127 |
Página de fin: | 148 |
DOI: | http://dx.doi.org/10.1016/S0167-2789(01)00355-4 |
Título revista: | Physica D: Nonlinear Phenomena |
Título revista abreviado: | Phys D Nonlinear Phenom |
ISSN: | 01672789 |
CODEN: | PDNPD |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01672789_v160_n3-4_p127_Brusch |