一类二维流场模型的周期解与浑沌解的共存性<sup>*</sup>

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

一类二维流场模型的周期解与浑沌解的共存性^*

基金项目: * 中国科学院科学基金

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

摘要: 本文研究Kelvin-Stuart猫眼流在周期扰动下的动力学行为,运用Melnikov方法确定出振动型周期轨产生偶数阶次谐分枝、旋转型周期轨产生任意阶次谐分枝的条件,并进一步发现周期解与浑沌解共存的复杂现象.
- 浑沌 /
- 分枝 /
- 横截 /
- 异宿环 /
- 同宿轨 /
- 猫眼流 /
- 涡旋
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

[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.