Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback

Weihua Jiang; Yuan Yuan

doi:10.1016/j.physd.2007.01.003

Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback

Weihua Jiang
, Yuan Yuan^*

^*Corresponding author for this work

School of Mathematics

Memorial University of Newfoundland

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

82 Scopus citations

Abstract

In this paper, we study the classical Van der Pol's equation with delayed feedback. We investigate the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state.

Original language	English
Pages (from-to)	149-161
Number of pages	13
Journal	Physica D: Nonlinear Phenomena
Volume	227
Issue number	2
DOIs	https://doi.org/10.1016/j.physd.2007.01.003
State	Published - 15 Mar 2007

Keywords

Bogdanov-Takens bifurcation
Delayed feedback
Normal form
Singularity
Van der Pol's equation

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10.1016/j.physd.2007.01.003

Cite this

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title = "Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback",

abstract = "In this paper, we study the classical Van der Pol's equation with delayed feedback. We investigate the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state.",

keywords = "Bogdanov-Takens bifurcation, Delayed feedback, Normal form, Singularity, Van der Pol's equation",

author = "Weihua Jiang and Yuan Yuan",

year = "2007",

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doi = "10.1016/j.physd.2007.01.003",

language = "英语",

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T1 - Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback

AU - Jiang, Weihua

AU - Yuan, Yuan

PY - 2007/3/15

Y1 - 2007/3/15

N2 - In this paper, we study the classical Van der Pol's equation with delayed feedback. We investigate the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state.

AB - In this paper, we study the classical Van der Pol's equation with delayed feedback. We investigate the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state.

KW - Bogdanov-Takens bifurcation

KW - Delayed feedback

KW - Normal form

KW - Singularity

KW - Van der Pol's equation

UR - https://www.scopus.com/pages/publications/33947589642

U2 - 10.1016/j.physd.2007.01.003

DO - 10.1016/j.physd.2007.01.003

M3 - 文章

AN - SCOPUS:33947589642

SN - 0167-2789

VL - 227

SP - 149

EP - 161

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 2

ER -

Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback

Abstract

Keywords

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