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Infinite Number Of Parameter Regions With Fractal Nonchaotic Attractors In A Piecewise Map

Author

Listed:
  • TAO CHENG

    (School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, P. R. China)

  • YONGXIANG ZHANG

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. China)

  • YUNZHU SHEN

    (School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi’an 710021, P. R. China)

Abstract

We identify a countable infinity of parameter regimes with strange nonchaotic attractors (SNAs). At the edge of each arc parameter area, there is an uncountable infinity of SNAs with torus intermittency. The mechanism for the creation of SNAs in different regime is induced by an n-frequency quasiperiodic orbit through a quasiperiodic analog of saddle-node bifurcation (Type-I intermittent route). We describe the transition between tori and SNAs by the largest Lyapunov exponent and phase diagram. These SNAs are characterized by the phase sensitivity exponents, rational approximations, singular-continuous spectra, and distribution of finite-time Lyapunov exponents.

Suggested Citation

  • Tao Cheng & Yongxiang Zhang & Yunzhu Shen, 2021. "Infinite Number Of Parameter Regions With Fractal Nonchaotic Attractors In A Piecewise Map," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-11, June.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:04:n:s0218348x21500870
    DOI: 10.1142/S0218348X21500870
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