Saddle-Nodes and Third-Order Saddles, Source, and Sink

In this chapter, (2×3)-equilibrium networks with saddle-source and saddle-sink and saddle and source (sink) plus paralleled hyperbolic and hyperbolic-secant flows are presented first and (2×2)-equilibrium networks of third-order saddle and source (sink) with paralleled hyperbolic and hyperbolic-secant flows are discussed. The saddle-source (sink) is the appearing and switching bifurcations for saddle and source (sink). The third-order saddles are the appearing bifurcation of saddle, source (sink), and saddle. The third-order source (sink) is the appearing bifurcation of source (sink), saddle, and source (sink). The inflection-sources (sinks) infinite-equilibriums are the switching bifurcations of a hyperbolic flow with a connected saddle and a hyperbolic-secant flow with a connected source (sink). The up-down and down-up saddle infinite-equilibriums are the switching bifurcations of a saddle-source and sink with separated hyperbolic and hyperbolic-secant flows. The third-order increasing and decreasing concave-source and sink infinite-equilibriums are the switching bifurcations for the third-order saddles and source (sink) with separated hyperbolic and hyperbolic-secant flows