Dynamics of two delay coupled van der Pol oscillators

作者：Li X^*; Ji JC; Hansen CH

来源：Mechanics Research Communications, 2006, 33(5): 614-627.

DOI：10.1016/j.mechrescom.2005.09.009

• non-linear dynamics
• coupled van der Pol oscillators
• time delay
• bifurcation
• stability

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.

• 出版日期2006-10
• 单位河北工业大学