Dynamic bifurcation of a modified Kuramotoben Sivashinsky equation with higher-order nonlinearity |
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Authors: | Huang Qiong-Wei and Tang Jia-Shi |
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Institution: | College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China |
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Abstract: | Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto—Sivashinsky equation with a higher-order nonlinearity μ(ux)puxx 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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Keywords: | Kuramoto—Sivashinsky equation centre manifold reduction dynamic bifurcation |
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