A parameter-perturbation method for chaos control to stabilizing UPOs

Alexander Jimenez-Triana, Guanrong Chen, Alain Gauthier

Research output: Contribution to journalArticle

  • 7 Citations

Abstract

A new method is developed for controlling chaos in discrete systems by perturbing one of its parameters in the neighborhood of an unstable periodic orbit (UPO). For 2-D systems, only two changes in the parameter value are needed in order to stabilize a UPO embedded in the chaotic attractor. The method is general and can be applied to any discrete chaotic system, in which a parameter is accessible and can be changed around a nominal value. To validate and visualize the applicability of the method, an electronic circuit is designed, which resembles the dynamics of the Hénon system, and the control scheme is successfully tested on this circuit. The experimental results show good performance of the method in the presence of noise in the signals, uncertainties in the model, and disturbances in the real circuit system.

LanguageEnglish
Article number7001219
Pages407-411
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Volume62
Issue number4
DOIs
Publication statusPublished - Apr 1 2015

Fingerprint

Chaos theory
Networks (circuits)
Orbits
Chaotic systems
Uncertainty

Keywords

  • Chaos Control
  • Chaotic Circuit
  • Discrete System
  • Hénon System
  • Parametric Perturbation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

A parameter-perturbation method for chaos control to stabilizing UPOs. / Jimenez-Triana, Alexander; Chen, Guanrong; Gauthier, Alain.

In: IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 62, No. 4, 7001219, 01.04.2015, p. 407-411.

Research output: Contribution to journalArticle

@article{0aaa48d99f6d487ea900b0aaacc9ac6e,
title = "A parameter-perturbation method for chaos control to stabilizing UPOs",
abstract = "A new method is developed for controlling chaos in discrete systems by perturbing one of its parameters in the neighborhood of an unstable periodic orbit (UPO). For 2-D systems, only two changes in the parameter value are needed in order to stabilize a UPO embedded in the chaotic attractor. The method is general and can be applied to any discrete chaotic system, in which a parameter is accessible and can be changed around a nominal value. To validate and visualize the applicability of the method, an electronic circuit is designed, which resembles the dynamics of the H{\'e}non system, and the control scheme is successfully tested on this circuit. The experimental results show good performance of the method in the presence of noise in the signals, uncertainties in the model, and disturbances in the real circuit system.",
keywords = "Chaos Control, Chaotic Circuit, Discrete System, H{\'e}non System, Parametric Perturbation",
author = "Alexander Jimenez-Triana and Guanrong Chen and Alain Gauthier",
year = "2015",
month = "4",
day = "1",
doi = "10.1109/TCSII.2014.2387553",
language = "English",
volume = "62",
pages = "407--411",
journal = "IEEE Transactions on Circuits and Systems II: Express Briefs",
issn = "1549-7747",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",

}

TY - JOUR

T1 - A parameter-perturbation method for chaos control to stabilizing UPOs

AU - Jimenez-Triana, Alexander

AU - Chen, Guanrong

AU - Gauthier, Alain

PY - 2015/4/1

Y1 - 2015/4/1

N2 - A new method is developed for controlling chaos in discrete systems by perturbing one of its parameters in the neighborhood of an unstable periodic orbit (UPO). For 2-D systems, only two changes in the parameter value are needed in order to stabilize a UPO embedded in the chaotic attractor. The method is general and can be applied to any discrete chaotic system, in which a parameter is accessible and can be changed around a nominal value. To validate and visualize the applicability of the method, an electronic circuit is designed, which resembles the dynamics of the Hénon system, and the control scheme is successfully tested on this circuit. The experimental results show good performance of the method in the presence of noise in the signals, uncertainties in the model, and disturbances in the real circuit system.

AB - A new method is developed for controlling chaos in discrete systems by perturbing one of its parameters in the neighborhood of an unstable periodic orbit (UPO). For 2-D systems, only two changes in the parameter value are needed in order to stabilize a UPO embedded in the chaotic attractor. The method is general and can be applied to any discrete chaotic system, in which a parameter is accessible and can be changed around a nominal value. To validate and visualize the applicability of the method, an electronic circuit is designed, which resembles the dynamics of the Hénon system, and the control scheme is successfully tested on this circuit. The experimental results show good performance of the method in the presence of noise in the signals, uncertainties in the model, and disturbances in the real circuit system.

KW - Chaos Control

KW - Chaotic Circuit

KW - Discrete System

KW - Hénon System

KW - Parametric Perturbation

UR - http://www.scopus.com/inward/record.url?scp=84927136915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927136915&partnerID=8YFLogxK

U2 - 10.1109/TCSII.2014.2387553

DO - 10.1109/TCSII.2014.2387553

M3 - Article

VL - 62

SP - 407

EP - 411

JO - IEEE Transactions on Circuits and Systems II: Express Briefs

T2 - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

SN - 1549-7747

IS - 4

M1 - 7001219

ER -