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Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation

1993; American Physical Society; Volume: 70; Issue: 25 Linguagem: Inglês

10.1103/physrevlett.70.3880

1092-0145

Stefan Popp, Olaf Stiller, Igor S. Aranson, Andreas Weber, Lorenz Kramer,

Slime Mold and Myxomycetes Research

The cubic complex Ginzburg-Landau equation is often used to model oscillatory media. In 1D it has a one-parameter family of moving ``hole'' solutions acting as sources for traveling waves (Nozaki and Bekki). We find that this family is destroyed by arbitrarily small generic perturbations leaving only the stationary phase-slip solutions. Its stability as well as the border of spatiotemporal chaos depend crucially on the sign of the perturbation. For ``stabilizing'' perturbations one also finds oscillations of the holes. The scenario can be modeled by the Van der Pol oscillator.