Cubic Dynamical Systems, Vol. IX Two-dimensional Two-product Cubic Systems with Different Product Structure Vector Fields

This book, the ninth of 15 related monographs, discusses a two product-cubic dynamical system possessing different product-cubic structures and the equilibrium and flow singularity and bifurcations for appearing and switching bifurcations. The appearing bifurcations herein are parabola-saddles, saddle-sources (sinks), hyperbolic-to-hyperbolic-secant flows, and inflection-source (sink) flows. The switching bifurcations for saddle-source (sink) with hyperbolic-to-hyperbolic-secant flows and parabola-saddles with inflection-source (sink) flows are based on the parabola-source (sink), parabola-saddles, inflection-saddles infinite-equilibriums. The switching bifurcations for the network of the simple equilibriums with hyperbolic flows are parabola-saddles and inflection-source (sink) on the inflection-source and sink infinite-equilibriums. Readers will learn new concepts, theory, phenomena, and analysis techniques.

· Two-different product-cubic systems

· Hybrid networks of higher-order equilibriums and flows

· Hybrid series of simple equilibriums and hyperbolic flows

· Higher-singular equilibrium appearing bifurcations

· Higher-order singular flow appearing bifurcations

· Parabola-source (sink) infinite-equilibriums

· Parabola-saddle infinite-equilibriums

· Inflection-saddle infinite-equilibriums

· Inflection-source (sink) infinite-equilibriums

· Infinite-equilibrium switching bifurcations.

• Develops a theory of nonlinear dynamics and singularity of two-different product-cubic dynamical systems;
• Presents networks of singular and simple equilibriums and hyperbolic flows in such different structure product-cubic systems;
• Reveals network switching bifurcations through infinite-equilibriums of parabola-source (sink) and parabola-saddles.

This book is the ninth of 15 related monographs, discusses a two product-cubic dynamical system possessing different product-cubic structures and the equilibrium and flow singularity and bifurcations for appearing and switching bifurcations. The appearing bifurcations herein are parabola-saddles, saddle-sources (sinks), hyperbolic-to-hyperbolic-secant flows, and inflection-source (sink) flows. The switching bifurcations for saddle-source (sink) with hyperbolic-to-hyperbolic-secant flows and parabola-saddles with inflection-source (sink) flows are based on the parabola-source (sink), parabola-saddles, inflection-saddles infinite-equilibriums. The switching bifurcations for the network of the simple equilibriums with hyperbolic flows are parabola-saddles and inflection-source (sink) on the inflection-source and sink infinite-equilibriums. Readers will learn new concepts, theory, phenomena, and analysis techniques.

· Two-different product-cubic systems

· Hybrid networks of higher-order equilibriums and flows

· Hybrid series of simple equilibriums and hyperbolic flows

· Higher-singular equilibrium appearing bifurcations

· Higher-order singular flow appearing bifurcations

· Parabola-source (sink) infinite-equilibriums

· Parabola-saddle infinite-equilibriums

· Inflection-saddle infinite-equilibriums

· Inflection-source (sink) infinite-equilibriums

· Infinite-equilibrium switching bifurcations.