Two-dimensional Product Cubic Systems, Vol. VII

This book, the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include:

. inflection-saddle infinite-equilibriums,

. hyperbolic-source (sink) infinite-equilibriums,

. up-down (down-up) saddle infinite-equilibriums,

. inflection-source (sink) infinite-equilibriums.

• Develops a theory of cubic dynamical systems possessing a product-cubic vector field and a self-quadratic vector field;
• Finds series/networks of equilibriums, 1-dimenional hyperbolic/hyperbolic-secant flows, finite-equilibrium switching;
• Presents sink and source separated by a connected hyperbolic-secant flow, and the (SO,SI) and (SI,SO)-saddles.