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Strange nonchaotic attractors in a class of quasiperiodically forced piecewise smooth systems

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Abstract

The existence of strange nonchaotic attractors (SNAs) and the associated mechanisms are studied in a class of quasiperiodically forced piecewise smooth systems. We show that the birth of SNAs is through interior crisis, basin boundary metamorphosis, discontinuous quasiperiodic orbits, and double bifurcation routes. Compared with the fractal, torus-doubling, and type-I intermittency routes, the four routes have more abundant dynamical phenomena, namely, the crisis-induced intermittency, the collision between attractors and the boundaries of fractal basin, the discontinuous quasiperiodic orbits, and the double bifurcation vertices. The characteristics of SNAs are described with the help of some qualitative and quantitative methods, such as the Lyapunov exponent, phase sensitivity function, critical exponent, and power spectrum.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12172340), Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics (Hubei University) (No. HBAM202201), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Nos. G1323523061, G1323523041), and the Young Top-notch Talent Cultivation Program of Hubei Province.

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Authors and Affiliations

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

    Jicheng Duan & Zhouchao Wei

  2. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Zhouchao Wei

  3. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, 066004, China

    Gaolei Li

  4. School of Mathematics and Statistic, Changshu Institute of Technology, Changshu, 215500, China

    Denghui Li

  5. Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Celso Grebogi

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  1. Jicheng Duan
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Jicheng Duan and Zhouchao Wei wrote the main manuscript text. Gaolei Li and Denghui Li prepared figures. Celso Grebogi checked the manuscript.

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Correspondence to Zhouchao Wei.

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Duan, J., Wei, Z., Li, G. et al. Strange nonchaotic attractors in a class of quasiperiodically forced piecewise smooth systems. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09678-6

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