The Duffing Equation: Periodic Solutions and Chaotic Dynamics (Infosys Science Foundation Series)

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Synopsis
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.
Copyright:
2025

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9789819783014
Related ISBNs:
9789819783007
Publisher:
Springer Nature Singapore
Date of Addition:
Copyrighted By:
The Editor
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Science, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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