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

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

Abstract

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.

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

• 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
• DOI: https://doi.org/10.1007/s11071-016-2857-3
• Keywords: Hidden dynamics; Two dimensional maps; Fixed point; Stability; Coexistence
• Public URL: http://hdl.handle.net/10059/1507