<p>In this paper, bursting oscillation of a four-dimensional electromechanical coupling transmission system is analyzed. The oscillations of the system are projected onto two subplanes. Four kinds of bursting modes are found by changing the parameters. It is found that fold bifurcation and Bogdanov-Takens bifurcation (BT) will cause trajectory jumping, and Hopf bifurcation will cause oscillation behavior of the system by transformed phase portraits. Meanwhile, we also find the slow channel effect. In addition, the Hankel Alternative View of Koopman (HAVOK) framework is first applied to analyze the bursting oscillations of electromechanical coupling transmission system. Then a forced linear model is used to approximate the strongly nonlinear system, which not only can reproduce the bursting oscillation phenomenon in two subplanes, but also find that the forced characteristic time series can characterize the occurrence of bursting oscillations. The intermittent burst correspond to the spiking state of the bursting oscillation. The optimal choice of truncation order and embedding dimension in the HAVOK framework will be considered in the furture.</p>