Constant and Self-Cubic Vector Fields

In this chapter, consider a cubic dynamical system possessing constant and variable-independent univariate cubic vector fields, and the corresponding dynamical behaviors and bifurcations are illustrated. The first- and third-order sink and source flows with upper-saddle and lower-saddle flows are obtained. The upper-saddle and lower-saddle flows are the switching and appearing bifurcations of sink and source flows. The third-order source flows are the appearing flows for the source, sink, and source flows. The third-order sink flows are the appearing flows for sink, source, and sink flows. The third-order source flows are the switching flows for source and saddle flows, and the third-order sink flows are the switching flows for sink and saddle flows.