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https://hdl.handle.net/2440/22870
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Type: | Journal article |
Title: | Dynamics of two delay coupled van der Pol oscillators |
Author: | Li, X. Ji, J. Hansen, C. |
Citation: | Mechanics Research Communications, 2006; 33(5):614-627 |
Publisher: | Pergamon-Elsevier Science Ltd |
Issue Date: | 2006 |
ISSN: | 0093-6413 1873-3972 |
Statement of Responsibility: | Xinye Li, J. C. Ji and Colin H. Hansen |
Abstract: | In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity coupling is studied by the method of averaging together with truncation of Taylor expansions. According to the slow-flow equations, the dynamics of 1:1 internal resonance is more complex than that of non-1:1 internal resonance. For 1:1 internal resonance, the stability and the number of periodic solutions vary with different time delay for given coupling coefficients. The condition necessary for saddle-node and Hopf bifurcations for symmetric modes, namely in-phase and out-of-phase modes, are determined. The numerical results, obtained from direct integration of the original equation, are found to be in good agreement with analytical predictions. |
Keywords: | non-linear dynamics coupled van der Pol oscillators time delay bifurcation stability |
DOI: | 10.1016/j.mechrescom.2005.09.009 |
Published version: | http://dx.doi.org/10.1016/j.mechrescom.2005.09.009 |
Appears in Collections: | Aurora harvest 2 Environment Institute publications Mechanical Engineering publications |
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