A quasi-analytical approach to period-doubling bifurcation computation and prediction

Daniel W. Berns; Jorge L. Moiola; Guanrong Chen

doi:10.23919/ECC.1999.7099331

A quasi-analytical approach to period-doubling bifurcation computation and prediction

Daniel W. Berns
, Jorge L. Moiola^*
, Guanrong Chen

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

3 Citations (Scopus)

Abstract

A quasi-analytical approach is developed in this paper for detecting the period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order harmonic balance approximations (HBAs) to compute the monodromy matrix, which is useful for the study of bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this computational procedure. An example is given to illustrate the main results, with an application to the delay control of the period-doubling bifurcation.

Original language	English
Title of host publication	European Control Conference, ECC 1999 - Conference Proceedings
Publisher	IEEE
Pages	373-378
ISBN (Print)	9783952417355
DOIs	https://doi.org/10.23919/ECC.1999.7099331
Publication status	Published - Aug 1999
Externally published	Yes
Event	1999 European Control Conference (ECC 1999) - Karlsruhe, Germany Duration: 31 Aug 1999 → 3 Sept 1999

Conference

Conference	1999 European Control Conference (ECC 1999)
Place	Germany
City	Karlsruhe
Period	31/08/99 → 3/09/99

Research Keywords

harmonic balance approximation
Hopf bifurcation
monodromy matrix
Period-doubling bifurcation

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10.23919/ECC.1999.7099331

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@inproceedings{004d9cc26d9b45078e77343587b6148e,

title = "A quasi-analytical approach to period-doubling bifurcation computation and prediction",

abstract = "A quasi-analytical approach is developed in this paper for detecting the period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order harmonic balance approximations (HBAs) to compute the monodromy matrix, which is useful for the study of bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this computational procedure. An example is given to illustrate the main results, with an application to the delay control of the period-doubling bifurcation.",

keywords = "harmonic balance approximation, Hopf bifurcation, monodromy matrix, Period-doubling bifurcation",

author = "Berns, \{Daniel W.\} and Moiola, \{Jorge L.\} and Guanrong Chen",

year = "1999",

month = aug,

doi = "10.23919/ECC.1999.7099331",

language = "English",

isbn = "9783952417355",

pages = "373--378",

booktitle = "European Control Conference, ECC 1999 - Conference Proceedings",

publisher = "IEEE",

address = "United States",

note = "1999 European Control Conference (ECC 1999) ; Conference date: 31-08-1999 Through 03-09-1999",

}

A quasi-analytical approach to period-doubling bifurcation computation and prediction. / Berns, Daniel W.; Moiola, Jorge L.; Chen, Guanrong.
European Control Conference, ECC 1999 - Conference Proceedings. IEEE, 1999. p. 373-378.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - A quasi-analytical approach to period-doubling bifurcation computation and prediction

AU - Berns, Daniel W.

AU - Moiola, Jorge L.

AU - Chen, Guanrong

PY - 1999/8

Y1 - 1999/8

N2 - A quasi-analytical approach is developed in this paper for detecting the period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order harmonic balance approximations (HBAs) to compute the monodromy matrix, which is useful for the study of bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this computational procedure. An example is given to illustrate the main results, with an application to the delay control of the period-doubling bifurcation.

AB - A quasi-analytical approach is developed in this paper for detecting the period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order harmonic balance approximations (HBAs) to compute the monodromy matrix, which is useful for the study of bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this computational procedure. An example is given to illustrate the main results, with an application to the delay control of the period-doubling bifurcation.

KW - harmonic balance approximation

KW - Hopf bifurcation

KW - monodromy matrix

KW - Period-doubling bifurcation

UR - https://www.scopus.com/pages/publications/84930579250

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84930579250&origin=recordpage

U2 - 10.23919/ECC.1999.7099331

DO - 10.23919/ECC.1999.7099331

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9783952417355

SP - 373

EP - 378

BT - European Control Conference, ECC 1999 - Conference Proceedings

PB - IEEE

T2 - 1999 European Control Conference (ECC 1999)

Y2 - 31 August 1999 through 3 September 1999

ER -

A quasi-analytical approach to period-doubling bifurcation computation and prediction

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