COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

Applied Mathematics and Mechanics (English Edition) ›› 1991, Vol. 12 ›› Issue (12): 1135-1142.

COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

袁晓凤¹, 郭瑞海²

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

收稿日期:1990-10-22 出版日期:1991-12-18 发布日期:1991-12-18
通讯作者: Kang Zhen-huang
基金资助:
Science Fund of the Chinese Academy of Sciences

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:1990-10-22 Online:1991-12-18 Published:1991-12-18
Supported by:
Science Fund of the Chinese Academy of Sciences

摘要/Abstract

摘要： 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.

关键词: chaos, bifurcation, transverse, heteroclinic cycle, homoclinic orbit, cat’s eye flow, vortex

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.

Key words: chaos, bifurcation, transverse, heteroclinic cycle, homoclinic orbit, cat’s eye flow, vortex

袁晓凤;郭瑞海. COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS[J]. Applied Mathematics and Mechanics (English Edition), 1991, 12(12): 1135-1142.

Yuan Xiao-feng;Guo Rui-hai. COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS[J]. Applied Mathematics and Mechanics (English Edition), 1991, 12(12): 1135-1142.

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COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

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