Dynamical Systems with Applications using Python

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. . 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. By Stephen Lynch. 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.-- Provided by publisher Front Matter ....Pages i-xvi A Tutorial Introduction to Python (Stephen Lynch)....Pages 1-31 Differential Equations (Stephen Lynch)....Pages 33-64 Planar Systems (Stephen Lynch)....Pages 65-94 Interacting Species (Stephen Lynch)....Pages 95-111 Limit Cycles (Stephen Lynch)....Pages 113-143 Hamiltonian Systems, Lyapunov Functions, and Stability (Stephen Lynch)....Pages 145-161 Bifurcation Theory (Stephen Lynch)....Pages 163-184 Three-Dimensional Autonomous Systems and Chaos (Stephen Lynch)....Pages 185-214 Poincaré Maps and Nonautonomous Systems in the Plane (Stephen Lynch)....Pages 215-243 Local and Global Bifurcations (Stephen Lynch)....Pages 245-269 The Second Part of Hilbert’s Sixteenth Problem (Stephen Lynch)....Pages 271-296 Delay Differential Equations (Stephen Lynch)....Pages 297-325 Linear Discrete Dynamical Systems (Stephen Lynch)....Pages 327-346 Nonlinear Discrete Dynamical Systems (Stephen Lynch)....Pages 347-384 Complex Iterative Maps (Stephen Lynch)....Pages 385-401 Electromagnetic Waves and Optical Resonators (Stephen Lynch)....Pages 403-432 Fractals and Multifractals (Stephen Lynch)....Pages 433-470 Image Processing with Python (Stephen Lynch)....Pages 471-489 Chaos Control and Synchronization (Stephen Lynch)....Pages 491-517 Neural Networks (Stephen Lynch)....Pages 519-555 Binary Oscillator Computing (Stephen Lynch)....Pages 557-589 Coursework and Examination-Type Questions (Stephen Lynch)....Pages 591-618 Solutions to Exercises (Stephen Lynch)....Pages 619-644 Back Matter ....Pages 645-665