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Dynamical Systems with Applications using Mathematica® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Mathematica’s symbolic, numerical, and graphical capabilities make it ideal for the study of nonlinear dynamical systems. An introductory chapter provides complete tutorials on how to use Mathematica’s text-based input commands and palettes, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at http://library.wolfram.com/infocenter/Books/AppliedMathematics/. Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Some of the material presented is at the postgraduate level and has been influenced by the author’s own research interests. Exercises are included at the end of every chapter. A comprehensive bibliography including textbooks and research papers rounds out the work. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work. Also by the author: Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8 Dynamical Systems with Applications using Maple, ISBN 978-0-8176-4150-4 .

Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential equations. --- Applied mathematics. --- Engineering mathematics. --- Statistical physics. --- Dynamical systems. --- Computational intelligence. --- Analysis. --- Applications of Mathematics. --- Ordinary Differential Equations. --- Statistical Physics, Dynamical Systems and Complexity. --- Appl.Mathematics/Computational Methods of Engineering. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- 517.1 Mathematical analysis --- Math --- Science --- Statistical methods --- Mathematica (Computer file) --- Differentiable dynamical systems --- Data processing. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Global analysis (Mathematics). --- Differential Equations. --- Engineering. --- Complex Systems. --- Mathematical and Computational Engineering. --- Construction --- Industrial arts --- Technology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox. Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems. Approximately 330 illustrations, over 300 examples, and exercises with solutions play a key role in the presentation. Over 60 MATLAB® program files and Simulink® model files are listed throughout the text; these files may also be downloaded from the Internet at: http://www.mathworks.com/matlabcentral/fileexchange/. Additional applications and further links of interest are also available at the author's website. The hands-on approach of Dynamical Systems with Applications using MATLAB® engages a wide audience of senior undergraduate and graduate students, applied mathematicians, engineers, and working scientists in various areas of the natural sciences. Reviews of the author’s published book Dynamical Systems with Applications using Maple®: "The text treats a remarkable spectrum of topics…and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple®." –U.K. Nonlinear News "…will provide a solid basis for both research and education in nonlinear dynamical systems." –The Maple Reporter.

Differentiable dynamical systems --- Dynamique différentiable --- Data processing --- Informatique --- MATLAB --- Surveillance --- monitoring --- Modèle dynamique --- Dynamic models --- Automatisation --- Automation --- Application des ordinateurs --- computer applications --- Logiciel --- Computer software --- Data processing. --- MATLAB. --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Geometry --- Engineering - General --- Dynamique différentiable --- Engineering. --- Applied mathematics. --- Engineering mathematics. --- Dynamics. --- Ergodic theory. --- Game theory. --- Statistical physics. --- Dynamical systems. --- Engineering, general. --- Applications of Mathematics. --- Dynamical Systems and Ergodic Theory. --- Game Theory, Economics, Social and Behav. Sciences. --- Complex Systems. --- Mathematical and Computational Engineering. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Games, Theory of --- Theory of games --- Mathematical models --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Engineering --- Engineering analysis --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Statistical methods

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This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite. Taking a hands-on approach, the reader is guided from basic concepts to modern research topics. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. The book begins with an efficient tutorial introduction to Mathematica, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at: http://library.wolfram.com/infocenter/Books/9563/ The author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum, though references are included for the inquisitive reader. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many of the chapters are especially useful as reference material for senior undergraduate independent project work. New to the second edition: Since the first printing of this book in 2007, Mathematica has evolved from version 6.0 to version 11.2 in 2017. Accordingly, the second edition has been thoroughly updated and new material has been added. There are many more applications, examples and exercises, all with solutions, and new sections on series solutions of ordinary differential equations and Newton fractals, have been added. There are also new chapters on delay differential equations, image processing, binary oscillator computing, and simulation with Wolfram SystemModeler. Praise for the first edition: “[This book’s] content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place.” —Dynamical Systems Magazine “This book presents an original, cheap and powerful solution to the problem of analysis of large data sets.” —Studia Universitatis Babes’-Bolyai Mathematica “The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.” —Datafile, The Journal of the HPCC.

Mathematics. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Computer software. --- Dynamical Systems and Ergodic Theory. --- Applications of Mathematics. --- Ordinary Differential Equations. --- Complex Systems. --- Mathematical and Computational Engineering. --- Mathematical Software. --- Differentiable dynamical systems. --- Differential Equations. --- Software, Computer --- Computer systems --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- Mathematica (Computer file) --- Statistical physics. --- Dynamical systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Statistical methods

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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. .

Differentiable dynamical systems. --- Differential Equations. --- Engineering mathematics. --- Mathematics. --- Statistical physics. --- Dynamical Systems and Ergodic Theory. --- Complex Systems. --- Ordinary Differential Equations. --- Mathematical and Computational Engineering. --- Applications of Mathematics. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Statistical methods --- Mathematics --- Python (Computer program language) --- Dynamics. --- Ergodic theory. --- Dynamical systems. --- Differential equations. --- Applied mathematics. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)

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This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox™, and the Symbolic Math Toolbox™, including MuPAD.   Features new to the second edition include   ·         sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; ·         chapters on image processing and binary oscillator computing; ·         hundreds of new illustrations, examples, and exercises with solutions; and ·         over eighty up-to-date MATLAB® program files and Simulink model files available online. These files were voted MATLAB® Central Pick of the Week in July 2013.   The hands-on approach of Dynamical Systems with Applications using MATLAB®, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics.                                          Praise for the first edition   Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing.  —OR News/Operations Research Spectrum   The MATLAB programs are kept as simple as possible and the author's experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes…. I recommend ‘Dynamical Systems with Applications using MATLAB’ as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering. —Mathematica.

Differential geometry. Global analysis --- Ergodic theory. Information theory --- Differential equations --- Mathematics --- Statistical physics --- Applied physical engineering --- Engineering sciences. Technology --- Matlab (informatica) --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde --- differentiaal geometrie --- theoretische fysica --- economie --- wiskunde --- ingenieurswetenschappen --- informatietheorie