國立高雄大學圖資館 |

Language: English

Back

Two-dimensional product-cubic systems.Vol.II,Product-quadratic vector fields

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two-dimensional product-cubic systems.by Albert C. J. Luo.
remainder title:	Product-quadratic vector fields
Author:	Luo, Albert C. J.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	ix, 292 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonlinear systems.
Online resource:	https://doi.org/10.1007/978-3-031-57116-9
ISBN:	9783031571169$q(electronic bk.)

Two-dimensional product-cubic systems.Vol.II,Product-quadratic vector fields
Luo, Albert C. J.

Two-dimensional product-cubic systems.Vol.II,Product-quadratic vector fields[electronic resource] /Product-quadratic vector fieldsby Albert C. J. Luo. - Cham :Springer Nature Switzerland :2024. - ix, 292 p. :ill. (some col.), digital ;24 cm.

Constant and Crossing-cubic Vector Fields -- Self-linear and Crossing-cubic Vector Fields -- Self-quadratic and Crossing-cubic Vector Fields.

This book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques. Product-quadratic and product cubic systems Self-linear and crossing-quadratic product vector fields Self-quadratic and crossing-linear product vector fields Hybrid networks of equilibriums and 1-dimensional flows Up-down and down-up saddle infinite-equilibriums Up-down and down-up sink-to-source infinite-equilibriums Inflection-source (sink) Infinite-equilibriums Diagonal inflection saddle infinite-equilibriums Infinite-equilibrium switching bifurcations Develops singularity and networks of equilibriums and 1-diemsnional flows in product-quadratic and cubic systems; Provides dynamics of product-quadratic/ product-cubic systems through equilibrium network and first integral manifolds; Discovers new switching bifurcations through infinite-equilibriums of up-down upper-saddles (lower-saddles)

ISBN: 9783031571169$q(electronic bk.)

Standard No.: 10.1007/978-3-031-57116-9doiSubjects--Topical Terms:

182906
Nonlinear systems.

LC Class. No.: QA402

Dewey Class. No.: 515.252

Two-dimensional product-cubic systems.Vol.II,Product-quadratic vector fields
LDR:03440nmm a2200361 a 4500 001 672041
003 DE-He213
005 20241111115721.0
006 m d
007 cr nn 008maaau
008 250325s2024 sz s 0 eng d
020 $a 9783031571169$q(electronic bk.)
020 $a 9783031571152$q(paper)
024 7 $a 10.1007/978-3-031-57116-9 $2 doi
035 $a 978-3-031-57116-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402
072 7 $a TBJ $2 bicssc
072 7 $a GPFC $2 bicssc
072 7 $a SCI064000 $2 bisacsh
072 7 $a TBJ $2 thema
072 7 $a GPFC $2 thema
082 0 4 $a 515.252 $2 23
090 $a QA402 $b .L964 2024
100 1 $a Luo, Albert C. J. $3 514321
245 1 0 $a Two-dimensional product-cubic systems. $n Vol.II, $p Product-quadratic vector fields $h [electronic resource] / $c by Albert C. J. Luo.
246 3 0 $a Product-quadratic vector fields
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a ix, 292 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Constant and Crossing-cubic Vector Fields -- Self-linear and Crossing-cubic Vector Fields -- Self-quadratic and Crossing-cubic Vector Fields.
520 $a This book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques. Product-quadratic and product cubic systems Self-linear and crossing-quadratic product vector fields Self-quadratic and crossing-linear product vector fields Hybrid networks of equilibriums and 1-dimensional flows Up-down and down-up saddle infinite-equilibriums Up-down and down-up sink-to-source infinite-equilibriums Inflection-source (sink) Infinite-equilibriums Diagonal inflection saddle infinite-equilibriums Infinite-equilibrium switching bifurcations Develops singularity and networks of equilibriums and 1-diemsnional flows in product-quadratic and cubic systems; Provides dynamics of product-quadratic/ product-cubic systems through equilibrium network and first integral manifolds; Discovers new switching bifurcations through infinite-equilibriums of up-down upper-saddles (lower-saddles)
650 0 $a Nonlinear systems. $3 182906
650 0 $a Equations, Cubic. $3 715927
650 0 $a Vector fields. $3 384687
650 0 $a Method of steepest descent (Numerical analysis) $3 191636
650 1 4 $a Applied Dynamical Systems. $3 913436
650 2 4 $a Mathematical and Computational Engineering Applications. $3 915034
650 2 4 $a Multibody Systems and Mechanical Vibrations. $3 922041
650 2 4 $a Stochastic Analysis. $3 922616
650 2 4 $a Integral Transforms and Operational Calculus. $3 913382
650 2 4 $a Dynamical Systems. $3 913342
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-57116-9
950 $a Engineering (SpringerNature-11647)