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Conservative chaos and invariant tori in the modified Sprott A system

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Abstract

Generally, there are few volume-conservative but not energy-conservative chaotic systems in the literature. By recomposing the skew-symmetric state matrix of the Sprott A system, a new volume-conservative chaotic system is coined in this paper. We mainly focus on investigating its dynamical behaviors that relay on the external excitation k, which directly determines the number of equilibria of the system. Without k, there exist two lines of equilibria that can be degenerated into two or four equilibria for the given nonzero initial conditions, while with k, the system is a no-equilibrium system that can produce conservative chaos and invariant tori for different initial conditions. Moreover, these rich dynamical behaviors are illustrated by several numerical techniques including time series, phase portraits, Poincaré sections, bifurcation diagrams and Lyapunov exponents.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (Grant No. 61873186), South African National Research Foundation (Grant Nos. 112142 and 112108), South African National Research Foundation Incentive Grant (No. 114911), and South African Eskom Tertiary Education Support Programme.

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Authors and Affiliations

  1. Department of Product Design, Tianjin University of Science and Technology, Tianjin, 300457, People’s Republic of China

    Shijian Cang

  2. College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin, 300222, People’s Republic of China

    Shijian Cang, Yue Li & Wei Xue

  3. Department of Electrical and Mining Engineering, University of South Africa, Florida, 1710, Republic of South Africa

    Zenghui Wang

  4. College of Artificial Intelligence, Nankai University, Tianjin, 300350, People’s Republic of China

    Zengqiang Chen

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  1. Shijian Cang
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  2. Yue Li
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  4. Zenghui Wang
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Correspondence to Shijian Cang.

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Cang, S., Li, Y., Xue, W. et al. Conservative chaos and invariant tori in the modified Sprott A system. Nonlinear Dyn 99, 1699–1708 (2020). https://doi.org/10.1007/s11071-019-05385-9

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  • DOI: https://doi.org/10.1007/s11071-019-05385-9

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