國立高雄大學圖資館 |

Language: English

Back

Limit cycles and homoclinic networks in two-dimensional polynomial systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Limit cycles and homoclinic networks in two-dimensional polynomial systemsby Albert C. J. Luo.
Author:	Luo, Albert C. J.
Published:	Singapore :Springer Nature Singapore :2025.
Description:	viii, 316 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Limit cycles.
Online resource:	https://doi.org/10.1007/978-981-97-2617-2
ISBN:	9789819726172$q(electronic bk.)

Limit cycles and homoclinic networks in two-dimensional polynomial systems
Luo, Albert C. J.

Limit cycles and homoclinic networks in two-dimensional polynomial systems[electronic resource] /by Albert C. J. Luo. - Singapore :Springer Nature Singapore :2025. - viii, 316 p. :ill., digital ;24 cm.

Introduction -- Homoclinic Networks without Centers -- Bifurcations for Homoclinic Networks without Centers -- Homoclinic Networks with Centers -- Bifurcations for Homoclinic Networks with Centers.

This book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert's sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering.

ISBN: 9789819726172$q(electronic bk.)

Standard No.: 10.1007/978-981-97-2617-2doiSubjects--Topical Terms:

561851
Limit cycles.

LC Class. No.: QA371

Dewey Class. No.: 515.35

Limit cycles and homoclinic networks in two-dimensional polynomial systems
LDR:02517nmm a2200325 a 4500 001 678099
003 DE-He213
005 20250418133515.0
006 m d
007 cr nn 008maaau
008 251021s2025 si s 0 eng d
020 $a 9789819726172$q(electronic bk.)
020 $a 9789819726165$q(paper)
024 7 $a 10.1007/978-981-97-2617-2 $2 doi
035 $a 978-981-97-2617-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371
072 7 $a GPFC $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA371 $b .L964 2025
100 1 $a Luo, Albert C. J. $3 514321
245 1 0 $a Limit cycles and homoclinic networks in two-dimensional polynomial systems $h [electronic resource] / $c by Albert C. J. Luo.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2025.
300 $a viii, 316 p. : $b ill., digital ; $c 24 cm.
505 0 $a Introduction -- Homoclinic Networks without Centers -- Bifurcations for Homoclinic Networks without Centers -- Homoclinic Networks with Centers -- Bifurcations for Homoclinic Networks with Centers.
520 $a This book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert's sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering.
650 0 $a Limit cycles. $3 561851
650 0 $a Polynomials. $3 184760
650 1 4 $a Dynamical Systems. $3 913342
650 2 4 $a Systems Theory, Control. $3 274654
650 2 4 $a Complex Systems. $3 558544
650 2 4 $a Differential Equations. $3 285983
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-97-2617-2
950 $a Mathematics and Statistics (SpringerNature-11649)