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

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

Authors

Haibo Jiang

Yang Liu

Zhouchao Wei

Liping Zhang



Abstract

This paper studies the hidden dynamics of a class of two-dimensional maps inspired by the H{acute}enon 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.

Journal Article Type Article
Publication Date Sep 1, 2016
Journal Nonlinear dynamics
Print ISSN 0924-090X
Electronic ISSN 1573-269X
Publisher Springer (part of Springer Nature)
Peer Reviewed Peer Reviewed
Volume 85
Issue 4
Pages 2719-2727
Institution Citation 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: https://doi.org/10.1007/s11071-016-2857-3
DOI https://doi.org/10.1007/s11071-016-2857-3
Keywords Hidden dynamics; Two dimensional maps; Fixed point; Stability; Coexistence

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