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Constructing chaotic systems with conditional symmetry

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Abstract

Asymmetric dynamical systems sometimes admit a symmetric pair of coexisting attractors for reasons that are not readily apparent. This phenomenon is called conditional symmetry and deserves further explanation and exploration. In this paper, a general method for constructing such systems is proposed in which the asymmetric system restores its original equation when some of the variables are subjected to a symmetric coordinate transformation combined with a special offset boosting. Two regimes of this conditional symmetry are illustrated in chaotic flows where a symmetric pair of attractors resides in asymmetric basins of attraction.

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Acknowledgments

C. Li wishes to thank J. Zha for helpful discussion. This work was supported financially by the Startup Foundation for Introducing Talent of NUIST (Grant No.: 2016205), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.:16KJB120004), the National Natural Science Foundation of China (Grant No.: 61072133), the Advantage Discipline “Information and Communication Engineering” of Jiangsu Province and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li & Hongyan Xing

  2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li & Hongyan Xing

  3. Department of Physics, University of Wisconsin–Madison, Madison, WI, 53706, USA

    Julien Clinton Sprott

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  1. Chunbiao Li
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  2. Julien Clinton Sprott
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  3. Hongyan Xing
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Correspondence to Chunbiao Li.

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Li, C., Sprott, J.C. & Xing, H. Constructing chaotic systems with conditional symmetry. Nonlinear Dyn 87, 1351–1358 (2017). https://doi.org/10.1007/s11071-016-3118-1

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  • DOI: https://doi.org/10.1007/s11071-016-3118-1

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