Simple Equilibrium Networks and Switching Dynamics

In this chapter, the simple equilibrium networks are presented for the cubic product system with two self-linear and crossing-quadratic product vector fields, and the corresponding inflection source and sink infinite equilibriums are for hyperbolic flows with paralleled saddle and center and for hyperbolic flows with connected saddle, source, and sink. The (3 × 3) simple equilibrium networks consist of negative and positive saddles, counterclockwise and clockwise centers, saddles, sink and source, and vertical and horizontal hyperbolic and hyperbolic secant flows. In addition, the double-switching bifurcations are generated through the inflection saddles formed by the two inflection source (sink) infinite equilibriums.