Self-Quadratic and Self-Cubic Vector Fields

In this chapter, a cubic dynamical system possessing independent-variable cubic and cubic vector fields will be discussed. The following equilibriums include simple sink, source, and saddles; saddle-source and saddle-sink; and third-order sink, saddle, and source, (2,2)-double-diagonal saddles, and (3,2)-saddle-source (sink). In addition to the appearing and switching bifurcations of the saddle-source (sink) and the third-order source, saddle, and sink, the appearing and switching bifurcations of the (2,2)-double diagonal saddles and (3,2)-saddle-source (sink) exist. The (2,2)-double diagonal saddles are for the appearing and switching bifurcations of a 2 × 2 network of sink, saddle, and source. (3,2)-saddle-source (sink) bifurcations are the appearing bifurcations of 3 × 2 network of sink, source, and source. The (3,2)-saddle-source (sink) are the switching bifurcations of the double-diagonal saddles with source, saddle, and sink. The (3,2)-saddle-source (sink) are also the appearing and switching bifurcations of the third-order source (sink) and third-order saddle.