Bifurcation analysis in a limit cycle oscillator with delayed feedback

Weihua Jiang; Junjie Wei

doi:10.1016/j.chaos.2004.05.028

Bifurcation analysis in a limit cycle oscillator with delayed feedback

Weihua Jiang
, Junjie Wei^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

23 Scopus citations

Abstract

A kind of limit cycle oscillator with delayed feedback is considered. Firstly, the linear stability is investigated. According to the analysis results, the bifurcation diagram is drawn in the parameter plane. It is found that there are stability switches for time delay, and Hopf bifurcations when time delay crosses through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the results found.

Original language	English
Pages (from-to)	817-831
Number of pages	15
Journal	Chaos, Solitons and Fractals
Volume	23
Issue number	3
DOIs	https://doi.org/10.1016/j.chaos.2004.05.028
State	Published - Feb 2005

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10.1016/j.chaos.2004.05.028

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title = "Bifurcation analysis in a limit cycle oscillator with delayed feedback",

abstract = "A kind of limit cycle oscillator with delayed feedback is considered. Firstly, the linear stability is investigated. According to the analysis results, the bifurcation diagram is drawn in the parameter plane. It is found that there are stability switches for time delay, and Hopf bifurcations when time delay crosses through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the results found.",

author = "Weihua Jiang and Junjie Wei",

year = "2005",

month = feb,

doi = "10.1016/j.chaos.2004.05.028",

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AU - Jiang, Weihua

AU - Wei, Junjie

PY - 2005/2

Y1 - 2005/2

N2 - A kind of limit cycle oscillator with delayed feedback is considered. Firstly, the linear stability is investigated. According to the analysis results, the bifurcation diagram is drawn in the parameter plane. It is found that there are stability switches for time delay, and Hopf bifurcations when time delay crosses through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the results found.

AB - A kind of limit cycle oscillator with delayed feedback is considered. Firstly, the linear stability is investigated. According to the analysis results, the bifurcation diagram is drawn in the parameter plane. It is found that there are stability switches for time delay, and Hopf bifurcations when time delay crosses through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the results found.

UR - https://www.scopus.com/pages/publications/4644296135

U2 - 10.1016/j.chaos.2004.05.028

DO - 10.1016/j.chaos.2004.05.028

M3 - 文章

AN - SCOPUS:4644296135

SN - 0960-0779

VL - 23

SP - 817

EP - 831

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 3

ER -

Bifurcation analysis in a limit cycle oscillator with delayed feedback

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