東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

The duffing equation = periodic solu...

Burra, Lakshmi.

Linked to FindBook

Google Book

Amazon

博客來

The duffing equation = periodic solutions and chaotic dynamics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The duffing equation/ by Lakshmi Burra, Fabio Zanolin.
Reminder of title:	periodic solutions and chaotic dynamics /
Author:	Burra, Lakshmi.
other author:	Zanolin, F.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xx, 259 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- The Autonomous Duffing Equation -- The Periodically Forced Duffing Equation -- Chaos in the Duffing Equation: With Some Simulations -- Topological Methods for the Detection of Chaos -- Applications to the Superlinear Duffing Equation -- Laser -- The Forced Pendulum -- Chaos in the Duffing-type Equation related to Tides -- Index.
Contained By:	Springer Nature eBook
Subject:	Duffing equations. -
Online resource:	https://doi.org/10.1007/978-981-97-8301-4
ISBN:	9789819783014

The duffing equation = periodic solutions and chaotic dynamics /
Burra, Lakshmi.

The duffing equationperiodic solutions and chaotic dynamics /[electronic resource] :by Lakshmi Burra, Fabio Zanolin. - Singapore :Springer Nature Singapore :2025. - xx, 259 p. :ill., digital ;24 cm. - Infosys science foundation series in mathematical sciences,2364-4044. - Infosys science foundation series in mathematical sciences..

Preface -- The Autonomous Duffing Equation -- The Periodically Forced Duffing Equation -- Chaos in the Duffing Equation: With Some Simulations -- Topological Methods for the Detection of Chaos -- Applications to the Superlinear Duffing Equation -- Laser -- The Forced Pendulum -- Chaos in the Duffing-type Equation related to Tides -- Index.

This book discusses the generalized Duffing equation and its periodic perturbations, with special emphasis on the existence and multiplicity of periodic solutions, subharmonic solutions and different approaches to prove rigorously the presence of chaotic dynamics. Topics in the book are presented at an expository level without entering too much into technical detail. It targets to researchers in the field of chaotic dynamics as well as graduate students with a basic knowledge of topology, analysis, ordinary differential equations and dynamical systems. The book starts with a study of the autonomous equation which represents a simple model of dynamics of a mechanical system with one degree of freedom. This special case has been discussed in the book by using an associated energy function. In the case of a centre, a precise formula is given for the period of the orbit by studying the associated period map. The book also deals with the problem of existence of periodic solutions for the periodically perturbed equation. An important operator, the Poincaré map, is introduced and studied with respect to the existence and multiplicity of its fixed points and periodic points. As a map of the plane into itself, complicated structure and patterns can arise giving numeric evidence of the presence of the so-called chaotic dynamics. Therefore, some novel topological tools are introduced to detect and rigorously prove the existence of periodic solutions as well as analytically prove the existence of chaotic dynamics according to some classical definitions introduced in the last decades. Finally, the rest of the book is devoted to some recent applications in different mathematical models. It carefully describes the technique of "stretching along the paths", which is a very efficient tool to prove rigorously the presence of chaotic dynamics.

ISBN: 9789819783014

Standard No.: 10.1007/978-981-97-8301-4doiSubjects--Topical Terms:

3780905
Duffing equations.

LC Class. No.: QA372

Dewey Class. No.: 515.355

The duffing equation = periodic solutions and chaotic dynamics /
LDR:03284nmm a2200337 a 4500 001 2408416
003 DE-He213
005 20250104115230.0
006 m o d
007 cr nn 008maaau
008 260204s2025 si s 0 eng d
020 $a 9789819783014 $q (electronic bk.)
020 $a 9789819783007 $q (paper)
024 7 $a 10.1007/978-981-97-8301-4 $2 doi
035 $a 978-981-97-8301-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA372
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.355 $2 23
090 $a QA372 $b .B968 2025
100 1 $a Burra, Lakshmi. $3 2107046
245 1 4 $a The duffing equation $h [electronic resource] : $b periodic solutions and chaotic dynamics / $c by Lakshmi Burra, Fabio Zanolin.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2025.
300 $a xx, 259 p. : $b ill., digital ; $c 24 cm.
490 1 $a Infosys science foundation series in mathematical sciences, $x 2364-4044
505 0 $a Preface -- The Autonomous Duffing Equation -- The Periodically Forced Duffing Equation -- Chaos in the Duffing Equation: With Some Simulations -- Topological Methods for the Detection of Chaos -- Applications to the Superlinear Duffing Equation -- Laser -- The Forced Pendulum -- Chaos in the Duffing-type Equation related to Tides -- Index.
520 $a This book discusses the generalized Duffing equation and its periodic perturbations, with special emphasis on the existence and multiplicity of periodic solutions, subharmonic solutions and different approaches to prove rigorously the presence of chaotic dynamics. Topics in the book are presented at an expository level without entering too much into technical detail. It targets to researchers in the field of chaotic dynamics as well as graduate students with a basic knowledge of topology, analysis, ordinary differential equations and dynamical systems. The book starts with a study of the autonomous equation which represents a simple model of dynamics of a mechanical system with one degree of freedom. This special case has been discussed in the book by using an associated energy function. In the case of a centre, a precise formula is given for the period of the orbit by studying the associated period map. The book also deals with the problem of existence of periodic solutions for the periodically perturbed equation. An important operator, the Poincaré map, is introduced and studied with respect to the existence and multiplicity of its fixed points and periodic points. As a map of the plane into itself, complicated structure and patterns can arise giving numeric evidence of the presence of the so-called chaotic dynamics. Therefore, some novel topological tools are introduced to detect and rigorously prove the existence of periodic solutions as well as analytically prove the existence of chaotic dynamics according to some classical definitions introduced in the last decades. Finally, the rest of the book is devoted to some recent applications in different mathematical models. It carefully describes the technique of "stretching along the paths", which is a very efficient tool to prove rigorously the presence of chaotic dynamics.
650 0 $a Duffing equations. $3 3780905
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Dynamical Systems. $3 3538746
700 1 $a Zanolin, F. $3 3780904
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Infosys science foundation series in mathematical sciences. $3 3518533
856 4 0 $u https://doi.org/10.1007/978-981-97-8301-4
950 $a Mathematics and Statistics (SpringerNature-11649)