Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows

Yuan Xiao-feng; Guo Rui-hai

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Yuan Xiao-feng, Guo Rui-hai. Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1067-1074.

Citation:

Yuan Xiao-feng, Guo Rui-hai. Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1067-1074.

Citation:

Yuan Xiao-feng, Guo Rui-hai. Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1067-1074.

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Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows

Yuan Xiao-feng¹,
Guo Rui-hai²

1.
Institute of Mathematical Sciences, Chengdu Branch, Academia Sinica, Chengdu;
2.
Southwest Institute for Nationalities, Chengdu

Received Date: 1990-10-22
Publish Date: 1991-12-15

Abstract

Abstract

This paper discusses the dynamic behavior of the Kelvin-Stuart cat's eye flow under periodic perturbations. By means of the Melnikov method the conditions to have bifurcations to subharmonics of even order for the oscillating orbits and to have bifurcations to subharmonics of any order for the rotating orbits are given, and further, the coexistence phenomena of the chaotic motions and periodic solutions are presented.
- chaos,
- bifurcation,
- transverse,
- heteroclinic cycle,
- homoclinic orbit,
- cat’s eye flow,
- vortex

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References(5)

References

[1]	Bertozzi,A.L.,Heteroclinic orbits and chaotic dynamics in planar fluid flows,SIAM.J.Math.Anal.,19,6(1988),1271-1293.
[2]	李继彬,《浑沌与Melnikov方法》,重庆大学出版社(1989).
[3]	Langebartel,R.G.,Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions,SIAM.J.Math.Anal.,11,3(1980),506-513.
[4]	Guckenheimer,J.and P.Holmes,Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields Springer-Verlag(1983).
[5]	Li Ji-bin and Wang Bao-hua,Chaos and subharmonic bifurcations in the periodically forced system of phase-locked loops,Annals of Differential Equations,5,4(1989),407-426.