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Dynamical bifurcation of the two dimensional Swift-Hohenberg equation with odd periodic condition

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  • In this article, we study the stability and dynamic bifurcation for the two dimensional Swift-Hohenberg equation with an odd periodic condition. It is shown that an attractor bifurcates from the trivial solution as the control parameter crosses the critical value. The bifurcated attractor consists of finite number of singular points and their connecting orbits. Using the center manifold theory, we verify the nondegeneracy and the stability of the singular points.
    Mathematics Subject Classification: Primary: 35B32, 35B41.


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