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Modulated Amplitude Waves and the Transition from Phase to Defect Chaos | | Lutz Brusch
; Martin G. Zimmermann
; Martin van Hecke
; Markus Baer
; Alessandro Torcini
; | | Date: |
31 Dec 1999 | | Journal: | Phys. Rev. Lett. 85, 86 (2000) DOI: 10.1103/PhysRevLett.85.86 | | 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 mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We introduce and describe periodic coherent structures of the CGLE, called Modulated Amplitude Waves (MAWs). MAWs of various period P occur naturally in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period P, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures occur which evolve toward defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation. | | Source: | arXiv, nlin.CD/0001068 | | Services: | Forum | Review | PDF | Favorites | |
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