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Hidden chaotic attractors in a class of two-dimensional maps.

Jiang, Haibo; Liu, Yang; Wei, Zhouchao; Zhang, Liping


Haibo Jiang

Yang Liu

Zhouchao Wei

Liping Zhang


This paper studies the hidden dynamics of a class of two-dimensional maps inspired by the Hénon map. A special consideration is made to the existence of fixed points and their stabilities in these maps. Our concern focuses on three typical scenarios which may generate hidden dynamics, i.e., no fixed point, single fixed point, and two fixed points. A computer search program is employed to explore the strange hidden attractors in the map. Our findings show that the basins of some hidden attractors are tiny, so the standard computational procedure for localization is unavailable. The schematic exploring method proposed in this paper could be generalized for investigating hidden dynamics of high-dimensional maps.


JIANG, H., LIU. Y., WEI, Z. and ZHANG, L. 2016. Hidden chaotic attractors in a class of two-dimensional maps. Nonlinear dynamics [online], 85(4), pages 2719-2727. Available from:

Journal Article Type Article
Acceptance Date May 14, 2016
Online Publication Date May 31, 2016
Publication Date Sep 30, 2016
Deposit Date Jun 7, 2016
Publicly Available Date Jun 1, 2017
Journal Nonlinear dynamics
Print ISSN 0924-090X
Electronic ISSN 1573-269X
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 85
Issue 4
Pages 2719-2727
Keywords Hidden dynamics; Two dimensional maps; Fixed point; Stability; Coexistence
Public URL


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