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Product details:
ISBN13:9783031484711
ISBN10:3031484711
Binding:Hardback
No. of pages:449 pages
Size:235x155 mm
Language:English
Illustrations: 1 Illustrations, black & white; 31 Illustrations, color
700
Category:

Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I

A Self-univariate Cubic Vector Field
 
Edition number: 2024
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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Short description:

This book, the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.
  • Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems;
  • Provides a new research direction in nonlinear dynamics community;
  • Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows.

Long description:

This book is the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

Table of Contents:

Chapter 1 Constant and Self-cubic Vector fields.- Chapter 2 Crossing-linear and Self-cubic Vector Fields.- Chapter 3 Crossing-quadratic and Self-Cubic Vector Fields.- Chapter 4 Two Single-variable Cubic Vector Fields.