Constant and Product-Cubic Systems

In this chapter, product-cubic systems with constant vector fields are discussed. The cubic dynamical systems possessing a constant vector field with self-linear and crossing-quadratic product are discussed first. The parabola parallel flows and back-to-back parabola source and sink exist, and the switches of source and sink exist. The inflection source and sink flows are for the appearing and switching bifurcations of the connected hyperbolic and hyperbolic-secant flows. Secondly, the dynamical systems with a constant vector field plus a crossing-linear and self-quadratic product vector field are discussed. The inflection parallel flows are for the upper and lower-saddles switches and the sink and source switches. The separated hyperbolic and hyperbolic-secant flows with sink and source flows exist, and the hyperbolic-to-hyperbolic-secant flows are for the appearing bifurcation of two separated hyperbolic and hyperbolic-secant flows.