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

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

中国物理B ›› 2011, Vol. 20 ›› Issue (9): 94701-094701.doi: 10.1088/1674-1056/20/9/094701

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

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

黄琼伟, 唐驾时

College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

收稿日期:2011-03-23 修回日期:2011-05-05 出版日期:2011-09-15 发布日期:2011-09-15

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

Huang Qiong-Wei(黄琼伟)^† and Tang Jia-Shi(唐驾时)

College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

Received:2011-03-23 Revised:2011-05-05 Online:2011-09-15 Published:2011-09-15

摘要/Abstract

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)^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.

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.

Key words: Kuramoto—Sivashinsky equation, centre manifold reduction, dynamic bifurcation

中图分类号: (Nonlinearity, bifurcation, and symmetry breaking)

47.20.Ky

02.30.Oz (Bifurcation theory) 05.45.-a (Nonlinear dynamics and chaos)

黄琼伟, 唐驾时. Dynamic bifurcation of a modified Kuramoto–Sivashinsky equation with higher-order nonlinearity[J]. 中国物理B, 2011, 20(9): 94701-094701.

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[J]. Chin. Phys. B, 2011, 20(9): 94701-094701.

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

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

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