Two-dimensional Crossing 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 and centers. · Develops a theory of crossing and product cubic systems with a self-linear and crossing-quadratic product vector field; · Presents singular equilibrium series with inflection-source (sink) flows and networks of simple equilibriums; · Shows equilibrium appearing bifurcations of (2,2)-double-inflection saddles and inflection-source (sink) flows.