Horizontally Paralleled Saddle-Source and Saddle-Sink

In this chapter, the horizontally paralleled saddle source and saddle sink with hyperbolic flow singularity exist in equilibrium networks, and the center or saddle with separated hyperbolic and hyperbolic secant flows are paralleled. The hyperbolic flow singularity is for the appearing bifurcation of the paralleled hyperbolic and hyperbolic secant flows. The switching bifurcations for center (saddle) with paralleled hyperbolic (hyperbolic secant) flow and saddle source (sink) with connected hyperbolic singular flows are discussed. In addition, the switching bifurcations of the saddle source (sink) with connected saddle source (sink) and the saddle and center with paralleled hyperbolic singular flows are discussed through infinite equilibriums.