Dynamics of two delay coupled van der Pol oscillators

Publisher:
Pergamon - Elsevier Ltd
Publication Type:
Journal Article
Citation:
Mechanics Research Communications, 2006, 33 (5), pp. 614 - 627
Issue Date:
2006-01
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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.
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