Saddle-Node Singularity and Bifurcation Dynamics

In this chapter, the appearing and switching bifurcations in self-linear and crossing-quadratic product system with a self-quadratic vector fields are discussed, and the corresponding network of equilibriums are presented. The inflection-source (sink) flows and saddle-source (sink) for the appearing bifurcations are presented first. The inflection upper-saddle and lower-saddle on the infinite equilibriums are for inflection-source (sink) flows with connected saddle-source (sink). The inflection-source (sink) flows with connected saddles, source, and sink are presented. The hyperbolic and hyperbolic-secant source (sink) are the switching bifurcations of the inflection-source (sink) flows with connected saddle, source, and sink. The up-down-to-down-up upper-saddle (lower-saddle) are the switching bifurcations of hyperbolic and hyperbolic-secant flows with connected saddle-source (sink). The series of connected hyperbolic and hyperbolic-secant flows with saddle, sink, and source are presented.