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

Crossing-linear and Self-quadratic Product Vector Field
 
Edition number: 1st ed. 2024
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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Short description:

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).



 




  • Develops a theory of crossing and product cubic systems with a self-linear and crossing-quadratic product vector field;

  • Presents singular equilibrium series with inflection-source (sink) flows and networks of simple equilibriums;

  • Shows equilibrium appearing bifurcations of (2,2)-double-inflection saddles and inflection-source (sink) flows.

Long description:

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).



 



 



 

Table of Contents:

Crossing and Product cubic Systems.- Double-inflection Saddles and Parabola-saddles.- Three Parabola-saddle Series and Switching Dynamics.- Parabola-saddles, (1:1) and (1:3)-Saddles and Centers.- Equilibrium Networks and Switching with Hyperbolic Flows.