Dynamics in a Van Der Pol Model with Delay

Chang Jin Xu; Pei Luan Li; Ling Yun Yao

doi:10.4028/www.scientific.net/AMM.204-208.4586

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 204-208Dynamics in a Van Der Pol Model with Delay

Dynamics in a Van Der Pol Model with Delay

Abstract:

In this paper, the dynamics of a van der pol model with delay are considered. It is shown that the asymptotic behavior depends crucially on the time delay parameter. By regarded the delay as a bifurcation parameter, we are particularly interested in the study of the Hopf bifurcation problem. The length of delay which preserves the stability of the equilibrium is calculated. Some numerical simulations for justifying the analytical findings are included.

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Periodical:

Applied Mechanics and Materials (Volumes 204-208)

Pages:

4586-4589

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.204-208.4586

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Online since:

October 2012

Authors:

Chang Jin Xu, Pei Luan Li, Ling Yun Yao

Keywords:

Delay, Hopf Bifurcation, Periodic Solution, Stability, Van Der Pol Model

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References

[1] B. Appelbe, D. Rachinskii, A. Zhezherun: Hopf bifurcation in a van der Pol type oscillator with magnetic hysteresis, Physica B: Condensed Matter, 403 (2-3) (2008) 301-304.

DOI: 10.1016/j.physb.2007.08.034

Google Scholar

[2] Hongbin Wang, Weihua Jiang: Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback, Journal of Mathematical Analysis and Applications, 368 (1) (2010) 9-18.

DOI: 10.1016/j.jmaa.2010.03.012

Google Scholar

[3] M.S. Fofana: Dimensional reduction of nonlinear time delay systems, International Journal of Mathematics and Mathematical Sciences, 2 (2005) (2005) 311-328.

DOI: 10.1155/ijmms.2005.311

Google Scholar

[4] Y. Kuang: Delay Differential Equations With Applications in Population Dynamics, Academic Press, INC, (1993).

Google Scholar

[5] J. Hale: Theory of Functional Differential Equation, Springer-Verlag, (1977).

Google Scholar

[6] H. Freedman, V. S. H. Rao: The trade-off between mutual interference and time lags in predator-prey systems, Bulletin of Mathematical Biology, 45 (6) (1983) 991-1004.

DOI: 10.1016/s0092-8240(83)80073-1

Google Scholar