Copyright © 2011 Xiaobing Zhou et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the van der Pol equation with discrete and distributed delays. Linear
stability of this equation is investigated by analyzing the transcendental characteristic equation of
its linearized equation. It is found that this equation undergoes a sequence of Hopf bifurcations
by choosing the discrete time delay as a bifurcation parameter. In addition, the properties of Hopf
bifurcation were analyzed in detail by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate and verify the theoretical analysis.