Modulated Amplitude Waves and the Transition from Phase to Defect Chaos

Details Modulated Amplitude Waves and the Transition from Phase to Defect Chaos Modulated Amplitude Waves and the Transition from Phase to Defect Chaos

2000-01-31

arxiv.org/abs/nlin/0001068v2

Phys. Rev. Lett. 85, 86 (2000)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 5 figures minor changes in the text

Scientific paper

10.1103/PhysRevLett.85.86

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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