Two-Dimensional Self and Product Cubic Systems, Vol. I: Self-Linear and Crossing-Quadratic Product Vector Field

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).