Study of universal constants of bifurcation in a chaotic sine map

Qian ZHANG; Yong XIANG; Zhenghang FAN; Chuang BI

doi:10.1109/ISCID.2013.158

Study of universal constants of bifurcation in a chaotic sine map

Qian ZHANG, Yong XIANG, Zhenghang FAN, Chuang BI

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

4 Citations (Scopus)

Abstract

The symmetry breaking bifurcation of a sine map is discussed when the control parameter in the sine map is chosen as a bifurcation parameter. Based on the sine map, the bifurcation points can be derived by the iterative map. Then, the stability of the system is enhanced by employing a cubic and a linear chaotic controller to exactly control the locations of the bifurcation points. Moreover, the universal constants of the chaotic system have been obtained by numerical simulation. The validity of the theoretical analysis is proved by the diagrams of bifurcation and Lyapunov exponent.

Original language	English
Title of host publication	Proceedings : 2013 Sixth International Symposium on Computational Intelligence and Design
Publisher	IEEE
Pages	177-180
Number of pages	4
ISBN (Print)	9780769550794
DOIs	https://doi.org/10.1109/ISCID.2013.158
Publication status	Published - Oct 2013
Externally published	Yes
Event	6th International Symposium on Computational Intelligence and Design, ISCID 2013 - Hangzhou, China Duration: 28 Oct 2013 → 29 Oct 2013

Conference

Conference	6th International Symposium on Computational Intelligence and Design, ISCID 2013
Country/Territory	China
City	Hangzhou
Period	28/10/13 → 29/10/13

Keywords

Chaos control
Sine map
Symmetry breaking bifurcation
Universal constant

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10.1109/ISCID.2013.158

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title = "Study of universal constants of bifurcation in a chaotic sine map",

abstract = "The symmetry breaking bifurcation of a sine map is discussed when the control parameter in the sine map is chosen as a bifurcation parameter. Based on the sine map, the bifurcation points can be derived by the iterative map. Then, the stability of the system is enhanced by employing a cubic and a linear chaotic controller to exactly control the locations of the bifurcation points. Moreover, the universal constants of the chaotic system have been obtained by numerical simulation. The validity of the theoretical analysis is proved by the diagrams of bifurcation and Lyapunov exponent.",

keywords = "Chaos control, Sine map, Symmetry breaking bifurcation, Universal constant",

author = "Qian ZHANG and Yong XIANG and Zhenghang FAN and Chuang BI",

year = "2013",

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doi = "10.1109/ISCID.2013.158",

language = "English",

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pages = "177--180",

booktitle = "Proceedings : 2013 Sixth International Symposium on Computational Intelligence and Design",

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TY - GEN

T1 - Study of universal constants of bifurcation in a chaotic sine map

AU - ZHANG, Qian

AU - XIANG, Yong

AU - FAN, Zhenghang

AU - BI, Chuang

PY - 2013/10

Y1 - 2013/10

N2 - The symmetry breaking bifurcation of a sine map is discussed when the control parameter in the sine map is chosen as a bifurcation parameter. Based on the sine map, the bifurcation points can be derived by the iterative map. Then, the stability of the system is enhanced by employing a cubic and a linear chaotic controller to exactly control the locations of the bifurcation points. Moreover, the universal constants of the chaotic system have been obtained by numerical simulation. The validity of the theoretical analysis is proved by the diagrams of bifurcation and Lyapunov exponent.

AB - The symmetry breaking bifurcation of a sine map is discussed when the control parameter in the sine map is chosen as a bifurcation parameter. Based on the sine map, the bifurcation points can be derived by the iterative map. Then, the stability of the system is enhanced by employing a cubic and a linear chaotic controller to exactly control the locations of the bifurcation points. Moreover, the universal constants of the chaotic system have been obtained by numerical simulation. The validity of the theoretical analysis is proved by the diagrams of bifurcation and Lyapunov exponent.

KW - Chaos control

KW - Sine map

KW - Symmetry breaking bifurcation

KW - Universal constant

UR - http://www.scopus.com/inward/record.url?scp=84901036409&partnerID=8YFLogxK

U2 - 10.1109/ISCID.2013.158

DO - 10.1109/ISCID.2013.158

M3 - Conference paper (refereed)

AN - SCOPUS:84901036409

SN - 9780769550794

SP - 177

EP - 180

BT - Proceedings : 2013 Sixth International Symposium on Computational Intelligence and Design

PB - IEEE

T2 - 6th International Symposium on Computational Intelligence and Design, ISCID 2013

Y2 - 28 October 2013 through 29 October 2013

ER -

Study of universal constants of bifurcation in a chaotic sine map

Abstract

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Keywords

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