Cubic Dynamical Systems, Vol. X

This book, the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also presented, specifically: · Inflection-saddle infinite-equilibriums, · Hyperbolic (hyperbolic-secant)-sink and source infinite-equilibriums · Up-down and down-up saddle infinite-equilibriums, · Inflection-source (sink) infinite-equilibriums. - Develops a theory of nonlinear dynamics and singularity of crossing-linear and self-quadratic product dynamical systems; - Shows hybrid networks of singular/simple equilibriums and hyperbolic flows in two same structure product-cubic systems; - Presents network switching bifurcations through infinite-equilibriums of inflection-saddles hyperbolic-sink and source.