Simple Equilibrium Series and Switching Dynamics

In this chapter, simple equilibrium series with connected hyperbolic flows are presented, and the corresponding switching dynamics are discussed through the inflection-source and sink infinite-equilibriums. The inflection-source is the switching bifurcation for a hyperbolic-secant flow with a connected source and for a hyperbolic flow with a connected saddle. The inflection-sink is the switching bifurcation for a hyperbolic-secant flow with connected sink and for a hyperbolic flow with a connected saddle. The double switching bifurcations are generated by the two inflection-source and sink infinite-equilibriums.