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

doi:10.1088/1674-1056/20/9/094701

Abstract Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto—Sivashinsky equation with a higher-order nonlinearity μ(u_x)^pu_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.

Keywords: Kuramoto—Sivashinsky equation centre manifold reduction dynamic bifurcation

Received: 23 March 2011
Revised: 05 May 2011
Accepted manuscript online:

PACS:	47.20.Ky	(Nonlinearity, bifurcation, and symmetry breaking)
	02.30.Oz	(Bifurcation theory)
	05.45.-a	(Nonlinear dynamics and chaos)

Cite this article:

Huang Qiong-Wei(黄琼伟) and Tang Jia-Shi(唐驾时) Dynamic bifurcation of a modified Kuramoto–Sivashinsky equation with higher-order nonlinearity 2011 Chin. Phys. B 20 094701

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[1]	Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction Li Yu-Mei(李玉梅) and Guan Xin-Ping(关新平). Chin. Phys. B, 2009, 18(8): 3355-3366.

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

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