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Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation | | Lutz Brusch
; Alessandro Torcini
; Martin van Hecke
; Martin G. Zimmermann
; Markus Baer
; | | Date: |
10 Apr 2001 | | Journal: | Physica D 160, 127 (2001) DOI: 10.1016/S0167-2789(01)00355-4 | | Subject: | Chaotic Dynamics; Pattern Formation and Solitons; Disordered Systems and Neural Networks; Fluid Dynamics; Dynamical Systems | nlin.CD cond-mat.dis-nn math.DS nlin.PS physics.flu-dyn | | 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 $
u approx 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 neighboring 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. | | Source: | arXiv, nlin.CD/0104029 | | Services: | Forum | Review | PDF | Favorites | |
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