Two-dimensional Product-Cubic Systems, Vol. IV

This book, the eighth of 15 related monographs, discusses a product-cubic dynamical system possessing a product-cubic vector field and a crossing-univariate quadratic vector field. It presents equilibrium singularity and bifurcation dynamics, and. the saddle-source (sink) examined is the appearing bifurcations for saddle and source (sink). The double-inflection saddle equilibriums are the appearing bifurcations of the saddle and center, and also the appearing bifurcations of the network of saddles and centers. The infinite-equilibriums for the switching bifurcations featured in this volume include: - Parabola-source (sink) infinite-equilibriums, - Inflection-source (sink) infinite-equilibriums, - Hyperbolic (circular) sink-to source infinite-equilibriums, - Hyperbolic (circular) lower-to-upper saddle infinite-equilibriums. - Develops a theory of cubic dynamical systems having a product-cubic vector field and a crossing-quadratic vector field; - Shows equilibriums and paralleled hyperbolic and hyperbolic-secant flows with switching though infinite-equilibriums; - Presents CCW and CW centers separated by a paralleled hyperbolic flow and positive and negative saddles.