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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
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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.

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Lutz Brusch, Martin G. Zimmermann, Martin van Hecke, Markus Baer, Alessandro Torcini. 2000-05-18. Modulated Amplitude Waves and the Transition from Phase to Defect Chaos. https://doi.org/10.1103/physrevlett.85.86

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