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Dynamic bifurcation of a modified Kuramoto-Sivashinsky equation with higher-order nonlinearity

黄琼伟  唐驾时  
【摘要】:Under the periodic boundary condition,dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity μ(u x) p u xx are investigated by using the centre manifold reduction procedure.The result shows that as the control parameter crosses a critical value,the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points.Furthermore,for cases in which the distances to the bifurcation points are small enough,one-order approximations to the bifurcation solutions are obtained.

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