Two Self-Cubic Vector Fields

In this chapter, a cubic dynamical system possessing two independent-variable 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 saddle, (3,2)-saddle-source (sink), and (3,3)-double-third-order source, saddle, and sink. The (3,3)-double third-order source, saddle, and sink are the appearing bifurcations of the 3 × 3 network of source, saddle, and sink. The (3,3)-double-third-order source, saddle, and sinks are the switching bifurcation of the (3,2) and (2,3)-saddle-source (sink) with source, saddle, and sink. The (3,3)-double-third-order source, saddle, and sinks are also the switching bifurcation of the (3,1) and (1,3)-source, saddle, and sink with (3,2) and (2,3)-saddle-source (sink).