In this chapter, parabola-saddle and hyperbolic singular flows in the crossing and product cubic systems are presented, and the corresponding switching dynamics are discussed through infinite equilibriums. The parabola-saddles are the appearing and switching bifurcations of a saddle and center. The third-order centers are the appearing bifurcations of a center, saddle, and center. The third-order saddles are the appearing bifurcations of a saddle, center, and saddle. The parabola-saddles on the inflection source and sink infinite equilibriums are the switching bifurcations of a saddle and a hyperbolic-secant flow with a center and hyperbolic flow, respectively. The parabola-hyperbolic sink-to-source on the parabola sink and source infinite equilibriums are the switching bifurcations of a parabola-saddle and a hyperbolic flow with another parabola-saddle with hyperbolic-secant flow. The third-order parabola-saddles are the switching bifurcations of a third-order saddle and a hyperbolic-secant flow with a third-order center and hyperbolic flow.