This paper aims at the pitchfork bifurcations of a three-dimensional system, in which each equation of the system contains a single quadratic cross-product term. The change of the number of equilibria of the system as one parameter varies near a critical value, i.e., the pitchfork bifurcations for one parameter, is analyzed. The stability of the equilibria generated by the pitchfork bifurcations is investigated as well.
