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Two-dimensional single-variable cubic nonlinear systems.Vol. II,A crossing-variable 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:	Crossing-variable cubic vector field
Author:	Luo, Albert C. J.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	ix, 240 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonlinear systems.
Online resource:	https://doi.org/10.1007/978-3-031-57108-4
ISBN:	9783031571084$q(electronic bk.)

Two-dimensional single-variable cubic nonlinear systems.Vol. II,A crossing-variable cubic vector field
Luo, Albert C. J.

Two-dimensional single-variable cubic nonlinear systems.Vol. II,A crossing-variable cubic vector field[electronic resource] /Crossing-variable cubic vector fieldby Albert C. J. Luo. - Cham :Springer Nature Switzerland :2024. - ix, 240 p. :ill. (chiefly color), digital ;24 cm.

Constant and Self-Cubic Vector fields -- Self-linear and Self-cubic vector fields -- Self-quadratic and self-cubic vector fields -- Two self-cubic vector fields.

This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. 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-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Explains infinite-equilibriums for the switching of the first-order sink and source flows.

ISBN: 9783031571084$q(electronic bk.)

Standard No.: 10.1007/978-3-031-57108-4doiSubjects--Topical Terms:

182906
Nonlinear systems.

LC Class. No.: QA613.619

Dewey Class. No.: 515.63

Two-dimensional single-variable cubic nonlinear systems.Vol. II,A crossing-variable cubic vector field
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520 $a This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. 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-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Explains infinite-equilibriums for the switching of the first-order sink and source flows.
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