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|Title:||Dynamics of two delay coupled van der Pol oscillators|
|Citation:||Mechanics Research Communications, 2006; 33(5):614-627|
|Publisher:||Pergamon-Elsevier Science Ltd|
|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|
|Appears in Collections:||Mechanical Engineering publications|
Environment Institute publications
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