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Hidden chaotic attractors in a class of two-dimensional maps

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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.

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Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable comments and suggestions that have helped to improve the presentation of the paper. This work is partially supported by the National Natural Science Foundation of China (Grant No. 11402224, 11202180, 61273106, 11171290, 11401543), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20151295), the Qin Lan Project of the Jiangsu Higher Education Institutions of China, the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers, the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUGL150419) and Presidents and the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, 224002, China

    Haibo Jiang & Liping Zhang

  2. School of Engineering, Robert Gordon University, Garthdee Road, Aberdeen, AB10 7GJ, UK

    Yang Liu

  3. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Zhouchao Wei

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  1. Haibo Jiang
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  2. Yang Liu
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  3. Zhouchao Wei
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  4. Liping Zhang
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Correspondence to Haibo Jiang.

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Jiang, H., Liu, Y., Wei, Z. et al. Hidden chaotic attractors in a class of two-dimensional maps. Nonlinear Dyn 85, 2719–2727 (2016). https://doi.org/10.1007/s11071-016-2857-3

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