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

Beschreibung

Back cover Materials

Albert C J Luo

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

Self-linear and crossing-quadratic product vector field

This book is 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.

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

•  double-inflection saddles, 
•  inflection-source (sink) flows,
•  parabola-saddles (saddle-center),
•  third-order parabola-saddles, 
•  third-order saddles (centers),
•  third-order saddle-source (sink).

Autor*in

Albert C. J. Luo

Themen in »Two-dimensional Self and Product Cubic Systems, Vol. I«

Crossing and product cubic systems Self-linear and crossing-quadratic product vector field Crossing-cubic vector field Hybrid series of singular equilibriums and flows Double-inflection saddles appearing bifurcations Inflection-source (sink) flows appearing bifurcations Parabola-saddles (saddle-center) appearing bifurcations Third-order parabola-saddles appearing bifurcations Third-order saddles (centers) appearing bifurcations Third-order saddle-source (sink) appearing bifurcations parabola-source (sink) infinite-equilibriums parabola-saddle infinite-equilibriums inflection-source (sink) infinite-equilibrium

Stimmen zu »Two-dimensional Self and Product Cubic Systems, Vol. I«

Details

Link teilen