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

This book, the twelfth of 15 related monographs on Cubic Systems, discusses self and product cubic systems with a self-linear and crossing-quadratic product vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed. The volume explains how the equilibrium series with connected hyperbolic and hyperbolic-secant flows exist in such cubic systems, and that the corresponding switching bifurcations are obtained through the inflection-source and sink infinite-equilibriums. Finally, the author illustrates how, in such cubic systems, the appearing bifurcations include saddle-source (sink) for equilibriums and inflection-source and sink flows for the connected hyperbolic flows, and the third-order saddle, sink and source are the appearing and switching bifurcations for saddle-source (sink) with saddles, source and sink, and also for saddle, sink and source. - Develops a theory of self and product cubic systems with a self-linear and crossing-quadratic product vector field; - Presents equilibrium series with flow singularity and connected hyperbolic and hyperbolic-secant flows; - Shows equilibrium series switching bifurcations through a range of sources and saddles on the infinite-equilibriums.