Self-Linear and Self-Cubic Vector Fields

In this chapter, a cubic dynamical system possessing self-linear and self-cubic vector fields is discussed. The corresponding equilibriums include simple sink, source, and saddles; saddle-source and saddle-sink; and third-order sink, saddle, and source. The saddle-source (sink) is for the appearing and switching bifurcations of saddle and source (sink). The third-order source, saddle, and sink are for the following four appearing and switching bifurcations: