INFINITE NUMBER OF PARAMETER REGIONS WITH FRACTAL NONCHAOTIC ATTRACTORS IN A PIECEWISE MAP

Tao Cheng, Yongxiang Zhang and Yunzhu Shen
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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

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-11

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.

Keywords: Strange Nonchaotic Attractor; Fractal; Nonsmooth System; Saddle-Node Bifurcation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500870

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