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Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling
List of Titles
Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling
Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/198840
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- Title
- Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling
- Author(s)
- Song, Yongli; Xu, Jian; Zhang, Tonghua
- Abstract
- In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences
- Source
- Chaos, Vol. 21, no. 2 (Jun 2011), article no. 023111
- Publication year
- 2011
- FOR Code(s)
- 0102 Applied Mathematics
- Keyword(s)
- Amplitude death; Bifurcations; Coupling time delay; Oscillations; van der Pol oscillators
- Publisher
- American Institute of Physics
- ISSN
- 1054-1500
- Publisher URL
- http://dx.doi.org/10.1063/1.3578046
- Copyright
- Copyright © 2011 American Institute of Physics. Published version of this paper reproduced here with the kind permission of the publisher.
- Research Projects
-
Approved wavelet approaches for solving nonlinear dynamic systems in process engineering, Australian Research Council grant number DP0770420
- Full text
- Peer reviewed
