Dynamical Systems with Applications using ...

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

Designed for a broad audience of students in applied mathematics, physics, and engineering

Represents dynamical systems with popular Python libraries like sympy, numpy, and matplotlib

Explores a variety of advanced topics in dynamical systems, like neural networks, fractals, and nonlinear optics, at an undergraduate level

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2019
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	684
Inhalt:	xvi 665 S. 159 s/w Illustr. 118 farbige Illustr. 665 p. 277 illus. 118 illus. in color.
ISBN-13:	9783030086244
ISBN-10:	3030086240
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Lynch, Stephen
Auflage:	Softcover reprint of the original 1st ed. 2018
Hersteller:	Springer International Publishing
Maße:	235 x 155 x 35 mm
Von/Mit:	Stephen Lynch
Erscheinungsdatum:	08.02.2019
Gewicht:	1,163 kg

preigu-id: 117480330