Two-dimensional Self and Product Cubic Systems, Vol. I

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

•  double-inflection saddles, 
•  inflection-source (sink) flows,
•  parabola-saddles (saddle-center),
•  third-order parabola-saddles, 
•  third-order saddles (centers),
•  third-order saddle-source (sink).