Equilibrium Networks and Switching Bifurcations

In this chapter, equilibrium networks with two connected hyperbolic and hyperbolic-secant flows are presented, and the corresponding switching bifurcations are discussed. The horizontal and vertical inflection-sink infinite-equilibriums exist for the switching bifurcations. On the infinite-equilibriums, there are the parabola-saddle and inflection-source (sink) bifurcations. Parabola-saddle switching bifurcations are for the hyperbolic flow with paralleled center, hyperbolic-secant flow with paralleled positive and negative saddles. The inflection-source (sink) switching bifurcations are for the hyperbolic flow with connected saddle and the hyperbolic-secant flow with connected source and sink. The double-inflection diagonal saddles are for the double switching bifurcations in the two directions.