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Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation. (English) Zbl 1197.35039
Summary: Stability and dynamic bifurcation in the ac-driven complex Ginzburg-Landau 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.

35B32Bifurcation (PDE)
35K20Second order parabolic equations, initial boundary value problems
37G10Bifurcations of singular points
35K58Semilinear parabolic equations
35B35Stability of solutions of PDE
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