Abstract
In this paper, the homotopy analysis method (HAM) is used to give series solutions of self-exited oscillation systems governed by two Van der Pol equations, which are coupled by a linear and a cubic term. The frequency and amplitude of all possible periodic solutions are investigated. It is found that there exist either in-phase or out-of-phase periodic solutions only. Besides, the in-phase periodic oscillations are decoupled, whose periods and amplitudes have nothing to do with the linear and cubic coupled terms. However, the out-of-phase periodic oscillations are strongly coupled, whose period and amplitude can be controlled by the linear and cubic coupled terms. (C) 2010 American Institute of Physics. [doi:10.1063/1.3445770]