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Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise

Author

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  • GAOLEI LI

    (Applied Mechanics and Structure, Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China)

  • YUAN YUE

    (��Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK)

  • CELSO GREBOGI

    (��Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK)

  • DENGHUI LI

    (��School of Mathematics and Statistics, Hexi University, Zhangye 734000, P. R. China)

  • JIANHUA XIE

    (�School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China)

Abstract

The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

Suggested Citation

  • Gaolei Li & Yuan Yue & Celso Grebogi & Denghui Li & Jianhua Xie, 2022. "Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-11, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500037
    DOI: 10.1142/S0218348X22500037
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    Cited by:

    1. Li, Gaolei & Li, Denghui & Wang, Chen & Yue, Yuan & Wen, Guilin & Grebogi, Celso, 2024. "Quantifying strange property of attractors in quasiperiodically forced systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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