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

Qiongwei Huang; Jiashi Tang

doi:10.3934/dcdsb.2010.14.129

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2010, Volume 14, Issue 1: 129-141. Doi: 10.3934/dcdsb.2010.14.129

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

Qiongwei Huang^1, and
Jiashi Tang^1,

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

Received: June 30, 2009

Revised: December 31, 2009

Published: June 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K20; Secondary: 37G10.

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

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