Two-dimensional Crossing and Product Cubic Systems, Vol. II

This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center). - Develops a theory of crossing and product cubic systems with a crossing-linear and self-quadratic product vector field; - Presents equilibrium series with hyperbolic-to-hyperbolic-scant flows and with paralleled hyperbolic flows; - Shows equilibrium series switching bifurcations by up-down hyperbolic upper-to-lower saddles, parabola-saddles, et al.