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A new set of hyperchaotic maps based on modulation and coupling

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Abstract

In this paper, a class of hyperchaotic mappings is constructed based on one-dimensional Logistic map and modulated coupling control methods. First, the equilibrium points of the system are analyzed using the M-SS map as an example and it is found that the M-SS map has infinite equilibrium points. Second, the dynamical characteristics of the newly constructed hyperchaotic maps are analyzed by means of phase diagram, bifurcation diagram, Lyapunov exponent spectrums and complexity. The analysis shows that the newly constructed class of hyperchaotic mappings has richer dynamical properties than the one-dimensional Logistic map, such as wider chaotic domains, hyperchaotic states and higher complexity. In addition, the DSP implementation of the hyperchaotic maps illustrates the feasibility of the class of chaotic maps in digital circuits.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62061014); The Natural Science Foundation of Liaoning Province (2020-MS-274); The Basic Scientific Research Projects of Colleges and Universities of Liaoning Province (Grant Nos. LJKZ0545).

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Authors and Affiliations

  1. School of mechanical engineering and automation, Dalian Polytechnic University, Dalian, 116034, China

    Xintong Han, Jun Mou, Yinghong Cao & Fanling Bu

  2. Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Canada

    Hadi Jahanshahi

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  1. Xintong Han
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  2. Jun Mou
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  3. Hadi Jahanshahi
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  4. Yinghong Cao
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Contributions

Xintong Han designed and carried out experiments, data analyzed and manuscript wrote. Jun Mou and Hadi Jahanshahi made the theoretical guidance for this paper. Yinghong Cao and Fanling Bu improved the algorithm. All authors reviewed the manuscript.

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Correspondence to Jun Mou or Fanling Bu.

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Han, X., Mou, J., Jahanshahi, H. et al. A new set of hyperchaotic maps based on modulation and coupling. Eur. Phys. J. Plus 137, 523 (2022). https://doi.org/10.1140/epjp/s13360-022-02734-3

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