Second and Third-Order Equilibriums

In this chapter, saddle-nodes (i.e., saddle-source and saddle-sink) and inflection-source and sink flows with saddle, source, and sink are discussed. The corresponding switching bifurcations are also discussed in this chapter. The saddle-source (sink) is the appearing bifurcation of saddle and source (sink). The inflection-source and sink flows are for the appearing bifurcations of the connected hyperbolic and hyperbolic-secant flows. In addition, the third-order saddles, source, and sink exist for the appearing bifurcations of saddle-nodes with source and sink, and they exist also for saddle, source, and sink. The switching bifurcations are through the inflection-saddle, parabola-source and sink, third-order trumpet source, and sink infinite-equilibriums. The inflection-saddles are for the switching bifurcations of saddle with inflection-source and sink flows. The hyperbolic-source and sink are the switching bifurcations of the inflection-source flow with source and the inflection-sink flow with sink, respectively. The hyperbolic-secant source and sink are the switching bifurcations of the inflection source and sink flows with saddles. The trumpet sink and source infinite-equilibriums are the switching bifurcations of the inflection-source and source with third-order saddle, sink, and source.