Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps

Denghui Li; Zhengbang  Cao; Xiaoming  Zhang; Celso Grebogi; Jianhua  Xie

doi:10.1142/S021812742150111X

Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps

Denghui Li, Zhengbang Cao^* (Corresponding Author), Xiaoming Zhang, Celso Grebogi, Jianhua Xie

^*Corresponding author for this work

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

3 Citations (Scopus)

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Abstract

In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

Original language	English
Article number	2150111
Number of pages	9
Journal	International Journal of Bifurcation and Chaos
Volume	31
Issue number	7
Early online date	15 Jun 2021
DOIs	https://doi.org/10.1142/S021812742150111X
Publication status	Published - 15 Jun 2021

Bibliographical note

Acknowledgments
This work is supported by the National Natural Science Foundation of China (11732014).

Keywords

strange nonchaotic attractors
skew product map
invariant graph

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10.1142/S021812742150111XLicence: Unspecified

Li_et_al_IJBC_StrangeNonchaoticAttractors_AAM
Electronic version of an article published as International Journal of Bifurcation and Chaos, Vol. 31, No. 7 (2021) 2150111 (9 pages) https://doi.org/10.1142/S021812742150111X © [copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijbc
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Cite this

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abstract = "In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.",

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AU - Cao, Zhengbang

AU - Zhang, Xiaoming

AU - Grebogi, Celso

AU - Xie, Jianhua

N1 - Acknowledgments This work is supported by the National Natural Science Foundation of China (11732014).

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Y1 - 2021/6/15

N2 - In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

AB - In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

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KW - skew product map

KW - invariant graph

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Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps

Abstract

Bibliographical note

Keywords

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