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A New Route to Strange Nonchaotic Attractors in an Interval Map

Yongxiang Zhang

http://orcid.org/0000-0001-6694-482X

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China

E-mail Address: zyx9701@126.com

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Yunzhu Shen

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China

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https://doi.org/10.1142/S0218127420500637Cited by:20 (Source: Crossref)

Abstract

We identify an unusual route to the creation of a strange nonchaotic attractor (SNA) in a quasiperiodically forced interval map. We find that the smooth quasiperiodic torus becomes nonsmooth due to the grazing bifurcation of the torus. The nonsmooth points on the torus increase more and more with the change of control parameter. Finally, the torus gets extremely fractal and becomes a SNA which is termed the grazing bifurcation route to the SNA. We characterize the SNA by maximal Lyapunov exponents and their variance, phase sensitivity exponents and power spectra. We also describe the transition between a torus and a SNA by the recurrence analysis. A remarkable feature of the route to SNAs is that the positive tails decay linearly and the negative tails exhibit recurrent fluctuations in the distribution of the finite-time Lyapunov exponents.

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References

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