Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation

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July 2010, 14(1): 129-141. doi: 10.3934/dcdsb.2010.14.129

Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation

1.	College of mechanics and aerospace, Hunan University, Changsha 410082, China, China

Received July 2009 Revised January 2010 Published April 2010

Abstract
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Stability and dynamic bifurcation in the ac-driven complex Ginzburg-Landau (GL) equation with periodic boundary conditions and even constraint are investigated using central manifold reduction procedure and attractor bifurcation theory. The results show that the bifurcation into an attractor near a small-amplitude limit cycle takes place on a two dimensional central manifold, as bifurcation parameter crosses a critical value. Furthermore, the component of the bifurcated attractor is analytically described for the non-autonomous system.

Keywords: Central manifold theorem., Ginzburg-Landau equation, Attractor bifurcation.

Mathematics Subject Classification: Primary: 35K20; Secondary: 37G1.

Citation: Qiongwei Huang, Jiashi Tang. Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 129-141. doi: 10.3934/dcdsb.2010.14.129

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