Dynamical Systems with Applications using Python

Stephen Lynch (Autor)

Buch | Softcover

XVI, 665 Seiten

2019
Springer International Publishing (Verlag)
978-3-030-08624-4 (ISBN)

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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.

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

Preface.- A Tutorial Introduction to Python.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincaré Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert's Sixteenth Problem.- Delay Differential Equations.- Linear Discrete Dynamical Systems.- Nonlinear Discrete Dynamical Systems.- Complex Iterative Maps.- Electromagnectic Waves and Optical Resonators.- Fractals and Multifractals.- Image Processing with Python.- Chaos Control and Synchronization.- Neural Networks.- Binary Oscillator Computing.- Coursework and Examination-Type Questions.- Solutions to Exercises.- Index of Python Programs.- Index.

"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)

Erscheinungsdatum	20.03.2022
Zusatzinfo	XVI, 665 p. 277 illus., 118 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1385 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Bifurcation Theory • chaos control and synchronization • Differential Equations • Fractals • GrÃ¶bner Bases • Gröbner Bases • Hamiltonian systems • limit cycles • Nonlinear discrete dynamical systems • optical resonators • Ordinary differential equations
ISBN-10	3-030-08624-0 / 3030086240
ISBN-13	978-3-030-08624-4 / 9783030086244
Zustand	Neuware