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© 2018

Dynamical Systems with Applications using Python

Textbook

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Stephen Lynch
    Pages 1-31
  3. Stephen Lynch
    Pages 33-64
  4. Stephen Lynch
    Pages 65-94
  5. Stephen Lynch
    Pages 95-111
  6. Stephen Lynch
    Pages 113-143
  7. Stephen Lynch
    Pages 163-184
  8. Stephen Lynch
    Pages 245-269
  9. Stephen Lynch
    Pages 297-325
  10. Stephen Lynch
    Pages 327-346
  11. Stephen Lynch
    Pages 347-384
  12. Stephen Lynch
    Pages 385-401
  13. Stephen Lynch
    Pages 403-432
  14. Stephen Lynch
    Pages 433-470
  15. Stephen Lynch
    Pages 471-489
  16. Stephen Lynch
    Pages 491-517

About this book

Introduction

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.

After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. 

This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential. 

Keywords

Gröbner bases nonlinear discrete dynamical systems bifurcation theory fractals optical resonators differential equations Hamiltonian systems limit cycles chaos control and synchronization

Authors and affiliations

  1. 1.Manchester Metropolitan UniversityManchesterUK

About the authors

Stephen Lynch is Senior Lecturer in the Department of Computing and Mathematics at Manchester Metropolitan University.

Bibliographic information

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Reviews

“Lynch has successfully captured this: I find this book to be uniquely successful in teaching a branch of mathematics together with computing while inspiring students to look at references and explorations beyond the text.” (Patrick Shipman, SIAM Review, Vol. 62 (2), 2020)

“This book is meant as an upper level undergraduate or graduate text in dynamical systems. … this is an attractive text, one that I wish I had access to when I was learning dynamical systems, and one that I would be glad to teach from.” (John Starrett, MAA Reviews, July 28, 2019)