Dynamical Systems with Applications Using Mathematica®

Description

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 Front Matter ....Pages i-xvi A Tutorial Introduction to Mathematica (Stephen Lynch)....Pages 1-15 Differential Equations (Stephen Lynch)....Pages 17-44 Planar Systems (Stephen Lynch)....Pages 45-72 Interacting Species (Stephen Lynch)....Pages 73-87 Limit Cycles (Stephen Lynch)....Pages 89-117 Hamiltonian Systems, Lyapunov Functions, and Stability (Stephen Lynch)....Pages 119-133 Bifurcation Theory (Stephen Lynch)....Pages 135-153 Three-Dimensional Autonomous Systems and Chaos (Stephen Lynch)....Pages 155-183 Poincaré Maps and Nonautonomous Systems in the Plane (Stephen Lynch)....Pages 185-208 Local and Global Bifurcations (Stephen Lynch)....Pages 209-230 The Second Part of Hilbert’s Sixteenth Problem (Stephen Lynch)....Pages 231-256 Delay Differential Equations (Stephen Lynch)....Pages 257-283 Linear Discrete Dynamical Systems (Stephen Lynch)....Pages 285-304 Nonlinear Discrete Dynamical Systems (Stephen Lynch)....Pages 305-338 Complex Iterative Maps (Stephen Lynch)....Pages 339-351 Electromagnetic Waves and Optical Resonators (Stephen Lynch)....Pages 353-380 Fractals and Multifractals (Stephen Lynch)....Pages 381-415 Image Processing and Analysis with Mathematica (Stephen Lynch)....Pages 417-428 Chaos Control and Synchronization (Stephen Lynch)....Pages 429-451 Neural Networks (Stephen Lynch)....Pages 453-484 Binary Oscillator Computing (Stephen Lynch)....Pages 485-507 An Introduction to Wolfram SystemModeler (Stephen Lynch)....Pages 509-522 Coursework and Examination-Type Questions (Stephen Lynch)....Pages 523-545 Solutions to Exercises (Stephen Lynch)....Pages 547-574 Back Matter ....Pages 575-585