Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise

L. I. Gaolei; Y. U.E. Yuan; Celso Grebogi; L. I. Denghui; X. I.E. Jianhua

doi:10.1142/S0218348X22500037

Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise

L. I. Gaolei, Y. U.E. Yuan^*, Celso Grebogi, L. I. Denghui, X. I.E. Jianhua

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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Abstract

The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

Original language	English
Article number	2250003
Number of pages	11
Journal	Fractals
Volume	30
Issue number	1
Early online date	13 Dec 2021
DOIs	https://doi.org/10.1142/S0218348X22500037
Publication status	Published - 2022

Bibliographical note

Acknowledgments
This work is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12072291, 11732014 and 12172306)

Keywords

Crisis
Intermittency
Noise
Piecewise Linear System
Strange Nonchaotic Attractor

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title = "Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise",

abstract = "The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.",

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author = "Gaolei, {L. I.} and Yuan, {Y. U.E.} and Celso Grebogi and Denghui, {L. I.} and Jianhua, {X. I.E.}",

note = "Acknowledgments This work is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12072291, 11732014 and 12172306)",

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AU - Yuan, Y. U.E.

AU - Grebogi, Celso

AU - Denghui, L. I.

AU - Jianhua, X. I.E.

N1 - Acknowledgments This work is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12072291, 11732014 and 12172306)

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Y1 - 2022

N2 - The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

AB - The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

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Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise

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