In this chapter, the authors show the existence of the Hopf bifurcation in the delayed
Liénard equation. The criterion for the criticality of the Hopf bifurcation is established
based on the reduction of the infinite-dimensional problem onto a twodimensional center
manifold. Numerics based on DDE-Biftool are given to compare with the authors’ theoretical
calculation. The Liénard type sunflower equation is discussed as an illustrative example
based on our method.