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Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

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  • Zhao, Yifan
  • Zhang, Yongxiang

Abstract

A new route to strange nonchaotic attractors (SNAs) is investigated in a quasiperiodically driven nonsmooth map. It is shown that the smooth quasiperiodic torus becomes nonsmooth (continuous and non-differentiable) due to the border-collision bifurcation of the torus. As the coefficients change, the nonsmooth torus gets gradually fractal, forming strange nonchaotic attractors. It is termed the border-collision bifurcation route to SNAs. A novel feature of this route is that a large number of SNAs are formed, and the parameter area of SNAs makes up about 40 % of the given parameter regions. These SNAs are identified by the largest Lyapunov exponents and the phase sensitivity exponents. They are also characterized by the distribution of finite-time Lyapunov exponents. Unlike other types of SNAs, the distribution of finite-time Lyapunov exponents has its maximum at a relatively small negative Lyapunov exponent, which contributes largely to lead to the abundance of SNAs.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003922
    DOI: 10.1016/j.chaos.2023.113491
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    References listed on IDEAS

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    1. Gaolei Li & Yuan Yue & Celso Grebogi & Denghui Li & Jianhua Xie, 2021. "Strange Nonchaotic Attractors And Multistability In A Two-Degree-Of-Freedom Quasiperiodically Forced Vibro-Impact System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-13, June.
    2. M., Paul Asir & K., Murali & P., Philominathan, 2019. "Strange nonchaotic attractors in oscillators sharing nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 83-93.
    3. 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.
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