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

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