Explosions of chaotic sets

被引:65
作者
Robert, C [1 ]
Alligood, KT
Ott, E
Yorke, JA
机构
[1] Univ Calif Santa Barbara, Dept Phys, Santa Barbara, CA 93106 USA
[2] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA
[3] Univ Maryland, Inst Plasma Res, Dept Phys, College Pk, MD 20742 USA
[4] Univ Maryland, Dept Elect Engn, College Pk, MD 20742 USA
[5] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA
[6] Univ Maryland, Dept Math, College Pk, MD 20742 USA
来源
PHYSICA D | 2000年 / 144卷 / 1-2期
关键词
explosion; chaos; tangency; bifurcation; recurrent;
D O I
10.1016/S0167-2789(00)00074-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Large-scale invariant sets such as chaotic attractors undergo bifurcations as a parameter is varied. These bifurcations include sudden changes in the size and/or type of the set. An explosion is a bifurcation in which new recurrent points suddenly appear at a non-zero distance from any pre-existing recurrent points. We discuss the following. In a generic one-parameter family of dissipative invertible maps of the plane there are only four known mechanisms through which an explosion can occur: (1) a saddle-node bifurcation isolated from other recurrent points, (2) a saddle-node bifurcation embedded in the set of recurrent points, (3) outer homoclinic tangencies, and (4) outer heteroclinic tangencies. (The term "outer tangency" refers to a particular configuration of the stable and unstable manifolds at tangency.) In particular, we examine different types of tangencies of stable and unstable manifolds from orbits of pre-existing invariant sets. This leads to a general theory that unites phenomena such as crises, basin boundary metamorphoses, explosions of chaotic saddles, etc. We illustrate this theory with numerical examples. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:44 / 61
页数:18
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