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

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


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