Two-dimensional Self and Product Cubic Systems Vol. I

<p>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:</p><ul> <li> double-inflection saddles </li> <li> inflection-source (sink) flows</li> <li> parabola-saddles (saddle-center)</li> <li> third-order parabola-saddles </li> <li> third-order saddles (centers)</li> <li> third-order saddle-source (sink).</li></ul><p> </p><p> </p><p> </p>