Vertical Saddle-Node Series and Switching Dynamics

In this chapter, three saddle-nodes (i.e., saddle-source, saddle-sink) series with a hyperbolic singular flow exist in self and product cubic systems. The hyperbolic singular flows are the appearing bifurcations for paralleled hyperbolic and hyperbolic flows. The saddle-source (sink) is the appearing bifurcation for saddle and source (sink). The inflection-source and sink infinite-equilibriums are for the switching bifurcations. The increasing and deceasing inflection-sources (sinks) are the switching bifurcations of the hyperbolic singular flows with saddle-sources (sinks).