Two-dimensional Self and Product Cubic Systems, Vol. I - Luo, Albert C. J.; - Prospero Internet Bookshop
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Two-dimensional Self and Product Cubic Systems, Vol. I: Self-linear and Crossing-quadratic Product Vector Field
 
Product details:
ISBN13:9783031570957
ISBN10:3031570952
Binding:Hardback
No. of pages:232 pages
Size:235x155 mm
Language:English
Illustrations: 1 Illustrations, black & white; 42 Illustrations, color
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Two-dimensional Self and Product Cubic Systems, Vol. I

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

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.

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.