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Two-dimensional single-variable cubic nonlinear systems.Vol. I,A self-univariate cubic vector field

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two-dimensional single-variable cubic nonlinear systems.by Albert C. J. Luo.
remainder title:	Self-univariate cubic vector field
Author:	Luo, Albert C. J.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	ix, 437 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonlinear systems.
Online resource:	https://doi.org/10.1007/978-3-031-48472-8
ISBN:	9783031484728$q(electronic bk.)

Two-dimensional single-variable cubic nonlinear systems.Vol. I,A self-univariate cubic vector field
Luo, Albert C. J.

Two-dimensional single-variable cubic nonlinear systems.Vol. I,A self-univariate cubic vector field[electronic resource] /Self-univariate cubic vector fieldby Albert C. J. Luo. - Cham :Springer Nature Switzerland :2024. - ix, 437 p. :ill. (chiefly color), digital ;24 cm.

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.

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.

ISBN: 9783031484728$q(electronic bk.)

Standard No.: 10.1007/978-3-031-48472-8doiSubjects--Topical Terms:

182906
Nonlinear systems.

LC Class. No.: QA613.619

Dewey Class. No.: 515.63

Two-dimensional single-variable cubic nonlinear systems.Vol. I,A self-univariate cubic vector field
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520 $a 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.
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