The local bifurcation of critical periods for the φ₆ field model

The local bifurcation of critical period problem for a nonlinear wave equation is discussed. Using the computer algebra system Mathematica,the period constants for the corresponding planar autonomous differential system are calculated. The necessary and sufficient condition for the origin to be one order weak center is obtained. It is proved that there is one local critical period bifurcation in the origin of the system. The result shows that the nonlinear wave equation has one local bifurcation of critical period.