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The duffing equationperiodic solutions and chaotic dynamics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The duffing equationby Lakshmi Burra, Fabio Zanolin.
其他題名:	periodic solutions and chaotic dynamics /
作者:	Burra, Lakshmi.
其他作者:	Zanolin, F.
出版者:	Singapore :Springer Nature Singapore :2025.
面頁冊數:	xx, 259 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Duffing equations.
電子資源:	https://doi.org/10.1007/978-981-97-8301-4
ISBN:	9789819783014$q(electronic bk.)

The duffing equationperiodic 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$q(electronic bk.)

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

992303
Duffing equations.

LC Class. No.: QA372

Dewey Class. No.: 515.355

The duffing equationperiodic solutions and chaotic dynamics /
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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.
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