Horizontally Connected Parabola-Saddles

In this chapter, horizontally connected parabola-saddles with paralleled inflection-source (sink) flow are discussed in a product cubic system possessing two self-linear and crossing-quadratic product vector fields. The inflection-source and sink flows exist for the appearing bifurcation of connected hyperbolic and hyperbolic-secant flows. The parabola-saddles are for the appearing bifurcations of saddle and center. The networks of connected parabola-saddles with separated inflection-source (sink) flow and connected hyperbolic and hyperbolic-secant flows with saddle, source, and sink are presented, and the corresponding switching bifurcations for such networks are presented through the vertical inflection-source (sink) and horizontal parabola-source (sink) infinite-equilibriums. The parabola-sinks and sources in the vertical and horizontal directions are obtained. The double-switching bifurcations are hyperbola source and sink with circle source-sink.