Double-Inflection-Saddles and Bifurcation Dynamics

In this chapter, double-inflection-saddles and bifurcation dynamics are discussed, and the corresponding phase portraits are illustrated. Double-inflection-saddles with paralleled inflection-source (sink) flows are presented. The parabola-sources (sinks) on the infinite-equilibrium are the switching bifurcations of double-inflection-saddles with paralleled inflection-source (sink) flows. The series of connected parabola-saddles with paralleled an inflection-source (sink) flow are presented. The connected hyperbolic flows paralleled with connected parabola-saddles are presented. The connected hyperbolic and circular, sink-to-source and source-to-sink on the parabola-source and sink infinite-equilibriums are presented for the switching bifurcations of connected hyperbolic flows with connected parabola-saddles. The network of saddles and centers paralleled with connected hyperbolic flows are presented, and the corresponding connected parabola-saddles are discussed for the switching bifurcation of hyperbolic flows with center and saddle.