Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-22
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay.
As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay.
Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity.
The results show that 1 : 2 resonance can lead to codimension-three and codimension-two bifurcations.
The validity of analytical predictions is shown by their consistency with numerical simulations.
American Psychological Association (APA)
Xu, Jian& Chung, K. W.. 2009. Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-16.
https://search.emarefa.net/detail/BIM-496515
Modern Language Association (MLA)
Xu, Jian& Chung, K. W.. Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities. Mathematical Problems in Engineering No. 2009 (2009), pp.1-16.
https://search.emarefa.net/detail/BIM-496515
American Medical Association (AMA)
Xu, Jian& Chung, K. W.. Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-16.
https://search.emarefa.net/detail/BIM-496515
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-496515