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Infinite-tori intermittency routes to strange nonchaotic attractors in a quasiperiodically forced piecewise-smooth system

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  • Shen, Yunzhu
  • Yu, Miao
  • Zhang, Yongxiang

Abstract

Quasiperiodically forced piecewise-smooth systems exhibit distinct routes to strange nonchaotic attractors (SNAs) through torus intermittency. This study reveals a novel infinite-tori intermittency route to SNA in a quasiperiodically forced piecewise-smooth linear system. Infinite n-frequency quasiperiodic tori transform into intermittent SNAs via an inverse period-adding bifurcation. The fractal structure of the attractor is verified through phase-space analysis, while its nonchaotic nature is identified by the largest Lyapunov exponent. Furthermore, we characterize the SNA using phase-sensitive exponents, recurrence plot topology and the distribution of finite-time Lyapunov exponents. In contrast to previously reported intermittent routes to SNAs, the distribution of finite-time Lyapunov exponents in this route exhibits a characteristic multi-peak distribution with zero-value. This work establishes infinite-tori-intermittency-induced SNA formation as a universal mechanism in quasiperiodically forced piecewise-smooth linear systems.

Suggested Citation

  • Shen, Yunzhu & Yu, Miao & Zhang, Yongxiang, 2025. "Infinite-tori intermittency routes to strange nonchaotic attractors in a quasiperiodically forced piecewise-smooth system," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925013190
    DOI: 10.1016/j.chaos.2025.117306
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    References listed on IDEAS

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    1. Yunzhu Shen & Wei Tang & Yungang Liu, 2022. "Tuning Of Imc Controller For Systems With Time-Delay Using An Improved Strange Nonchaotic Optimization Approach," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-11, December.
    2. Yunzhu Shen & Wei Tang, 2022. "Tuning Of Two-Degree-Of-Freedom Imc Based On A Strange Nonchaotic Optimization Approach For Large Time-Delay Processes," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-13, May.
    3. Zhao, Yifan & Zhang, Yongxiang, 2023. "Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Arulgnanam, A. & Prasad, Awadhesh & Thamilmaran, K. & Daniel, M., 2015. "Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with experimental and analytical confirmation," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 96-110.
    5. Yunzhu Shen & Yongxiang Zhang & Huidong Xu, 2021. "Strange Nonchaotic Attractors In A Quasiperiodically Forced Articulated Mooring Tower Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-14, December.
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