Chaos induced by regular snap-back repellers

被引：40

作者：

Shi, Yuming ^{[1
]}

Yu, Pei ^{[2
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

[2] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 337卷 / 02期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

chaos; snap-back repeller; coupled-expanding map;

D O I：

10.1016/j.jmaa.2007.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic orbit to a regular expanding fixed point in finite-dimensional spaces imply chaos in the sense of Li-Yorke. An illustrative example is provided with computer simulations. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：1480 / 1494

页数：15

共 31 条

[1] ON DEVANEY DEFINITION OF CHAOS [J].

BANKS, J ;

BROOKS, J ;

CAIRNS, G ;

DAVIS, G ;

STACEY, P .

AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (04) :332-334

[2]

Blanchard F, 2002, J REINE ANGEW MATH, V547, P51

[3]

BLOCK LS, 1992, LECT NOTES MATH, V1513, pUR3

[4] Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span [J].

Chen, G ;

Hsu, SB ;

Zhou, JX .

JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (12) :6459-6489

[5] Strange attractors in chaotic neural networks [J].

Chen, Luonan ;

Aihara, Kazuyuki .

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2000, 47 (10) :1455-1468

[6] Transversal homoclinic orbits in a transiently chaotic neural network [J].

Chen, SS ;

Shih, CW .

CHAOS, 2002, 12 (03) :654-671

[7]

Devaney R, 1987, An introduction to chaotic dynamical systems, DOI 10.2307/3619398

[8]

Diemling K., 1985, NONLINEAR FUNCTIONAL

[9] OCCURRENCE OF CHAOS IN HIGHER-DIMENSIONAL DISCRETE-TIME-SYSTEMS [J].

DOHTANI, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (06) :1707-1721

[10]

Elaydi SN, 2000, Discrete chaos

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