Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays
Joint Authors
Jiang, Murong
Zhou, Xiaobing
Cai, Xiaomei
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-05-12
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We consider the van der Pol equation with discrete and distributed delays.
Linear stability of this equation is investigated by analyzing the transcendental characteristic equation of its linearized equation.
It is found that this equation undergoes a sequence of Hopf bifurcations by choosing the discrete time delay as a bifurcation parameter.
In addition, the properties of Hopf bifurcation were analyzed in detail by applying the center manifold theorem and the normal form theory.
Finally, some numerical simulations are performed to illustrate and verify the theoretical analysis.
American Psychological Association (APA)
Zhou, Xiaobing& Jiang, Murong& Cai, Xiaomei. 2011. Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays. Discrete Dynamics in Nature and Society،Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-481468
Modern Language Association (MLA)
Zhou, Xiaobing…[et al.]. Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays. Discrete Dynamics in Nature and Society No. 2011 (2011), pp.1-16.
https://search.emarefa.net/detail/BIM-481468
American Medical Association (AMA)
Zhou, Xiaobing& Jiang, Murong& Cai, Xiaomei. Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays. Discrete Dynamics in Nature and Society. 2011. Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-481468
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-481468
