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Bifurcation analysis of the damped Kuramoto-Sivashinsky equation with respect to the period

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  • In this paper, we study bifurcation of the damped Kuramoto-Sivashinsky equation on an odd periodic interval of period $2\lambda$. We fix the control parameter $\alpha \in (0,1)$ and study how the equation bifurcates to attractors as $\lambda$ varies. Using the center manifold analysis, we prove that the bifurcated attractors are homeomorphic to $S^1$ and consist of four or eight singular points and their connecting orbits. We verify the structure of the bifurcated attractors by investigating the stability of each singular point.
    Mathematics Subject Classification: Primary: 37G35, 35B32.


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