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Bifurcation Behavior of a Modified Kuramoto-Sivashinsky Equation in Two-Dimensional Spatial Domain

Q. W. Huang, T. S. Tang, W. B. Fu, L. Zhang


The bifurcation behavior and stability of a modified Kuramoto-Sivashinsky equation in two dimensional spatial domain are investigated. When parameters of nonlinear items are small and the system is limited in the even function space, we obtain the reduced equation of the system and discuss the stability of the structure with multi-singular points by using the center manifold theorem. As the control parameter is changed, an attractor consisting of nontrivial steady state solutions is bifurcated. It is shown that phase transition arises in a two-dimensional growth interface between two stable states.


Bifurcation, Kuramoto-Sivashinsky equation, center manifold reduction, attractor.

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