Dynamical Systems with Applications using Mathematica:Dynamical Systems with Applications using Mathematica
Author(s): Stephen Lynch
Publisher: Birkhauser Boston; 1 edition
Date : 2007
Pages : 1
Format : PDF
OCR : Yes
Quality :
Language : English
ISBN-10 : 0817644822
ISBN-13 :
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.
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. Exercises are included at the end of every chapter. Both textbooks and research papers are presented in the list of references.
Working Mathematica notebooks will be available at
http://library.wolfram.com/infocenter/Books/AppliedMathematics/.
The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. The material is also accessible to readers with a general mathematical background. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work.
Review
"Stephen Lynch's book offers a comprehensive introduction to the theory and application of differential equations and dynamical systems methods. Its focus on applications and avoidance of overly technical arguments makes it a an equally good choice for teaching an undergraduate course in dynamical systems, as self-study for graduate students interested in dynamical systems, or as an introductory text for researchers seeking an overview of some current developments in applied dynamical systems. Most importantly, its content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place." —Dynamical Systems Magazine
Contents
Preface xi
0 ATutorial Introduction to Mathematica 1
0.1 A Quick Tour of Mathematica . . . . . . . . . . . . . . . . . . . 2
0.2 Tutorial One: The Basics (One Hour) . . . . . . . . . . . . . . . 4
0.3 Tutorial Two: Plots and Differential Equations (One Hour) . . . 6
0.4 The Manipulate Command and Simple Mathematica Programs . 8
0.5 Hints for Programming . . . . . . . . . . . . . . . . . . . . . . 11
0.6 Mathematica Exercises . . . . . . . . . . . . . . . . . . . . . . 12
1 Differential Equations 17
1.1 Simple Differential Equations and Applications . . . . . . . . . 18
1.2 Applications to Chemical Kinetics . . . . . . . . . . . . . . . . 25
1.3 Applications to Electric Circuits . . . . . . . . . . . . . . . . . 29
1.4 Existence and Uniqueness Theorem . . . . . . . . . . . . . . . . 32
1.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 35
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 Planar Systems 41
2.1 Canonical Forms . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2 Eigenvectors Defining Stable and Unstable Manifolds . . . . . . 46
2.3 Phase Portraits of Linear Systems in the Plane . . . . . . . . . . 49
vi Contents
2.4 Linearization and Hartman抯 Theorem . . . . . . . . . . . . . . 54
2.5 Constructing Phase Plane Diagrams . . . . . . . . . . . . . . . 55
2.6 Mathematica Commands in Text Format . . . . . . . . . . . . . 64
2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3 Interacting Species 69
3.1 Competing Species . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Predator朠rey Models . . . . . . . . . . . . . . . . . . . . . . . 72
3.3 Other Characteristics Affecting Interacting Species . . . . . . . 78
3.4 Mathematica Commands in Text Format . . . . . . . . . . . . . 80
3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 Limit Cycles 85
4.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . 86
4.2 Existence and Uniqueness of Limit Cycles in the Plane . . . . . 89
4.3 Nonexistence of Limit Cycles in the Plane . . . . . . . . . . . . 95
4.4 Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . 98
4.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 106
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 Hamiltonian Systems, Lyapunov Functions, and Stability 111
5.1 Hamiltonian Systems in the Plane . . . . . . . . . . . . . . . . . 112
5.2 Lyapunov Functions and Stability . . . . . . . . . . . . . . . . . 117
5.3 Mathematica Commands in Text Format . . . . . . . . . . . . . 122
5.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6 Bifurcation Theory 127
6.1 Bifurcations of Nonlinear Systems in the Plane . . . . . . . . . . 128
6.2 Normal Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3 Multistability and Bistability . . . . . . . . . . . . . . . . . . . 137
6.4 Mathematica Commands in Text Format . . . . . . . . . . . . . 140
6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7 Three-Dimensional Autonomous Systems and Chaos 145
7.1 Linear Systems and Canonical Forms . . . . . . . . . . . . . . . 146
7.2 Nonlinear Systems and Stability . . . . . . . . . . . . . . . . . 150
7.3 The R鰏sler System and Chaos . . . . . . . . . . . . . . . . . . 154
7.4 The Lorenz Equations, Chua抯 Circuit, and the
Belousov朲habotinski Reaction . . . . . . . . . . . . . . . . . 158
7.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 165
7.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8 Poincar?Maps and Nonautonomous Systems in the Plane 171
8.1 Poincar?Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Contents vii
8.2 Hamiltonian Systems with Two Degrees of Freedom . . . . . . . 178
8.3 Nonautonomous Systems in the Plane . . . . . . . . . . . . . . 181
8.4 Mathematica Commands in Text Format . . . . . . . . . . . . . 189
8.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
9 Local and Global Bifurcations 195
9.1 Small-Amplitude Limit Cycle Bifurcations . . . . . . . . . . . . 196
9.2 Gr鯾ner Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
9.3 Melnikov Integrals and Bifurcating Limit Cycles from a
Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
9.4 Bifurcations Involving Homoclinic Loops . . . . . . . . . . . . 209
9.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 211
9.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10 The Second Part of Hilbert抯 Sixteenth Problem 217
10.1 Statement of Problem and Main Results . . . . . . . . . . . . . 218
10.2 Poincar?Compactification . . . . . . . . . . . . . . . . . . . . 220
10.3 Global Results for Li閚ard Systems . . . . . . . . . . . . . . . . 227
10.4 Local Results for Li閚ard Systems . . . . . . . . . . . . . . . . 235
10.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
11 Linear Discrete Dynamical Systems 241
11.1 Recurrence Relations . . . . . . . . . . . . . . . . . . . . . . . 242
11.2 The Leslie Model . . . . . . . . . . . . . . . . . . . . . . . . . 247
11.3 Harvesting and Culling Policies . . . . . . . . . . . . . . . . . . 251
11.4 Mathematica Commands in Text Format . . . . . . . . . . . . . 255
11.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
12 Nonlinear Discrete Dynamical Systems 261
12.1 The Tent Map and Graphical Iterations . . . . . . . . . . . . . . 262
12.2 Fixed Points and Periodic Orbits . . . . . . . . . . . . . . . . . 266
12.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum
Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
12.4 Gaussian and H閚on Maps . . . . . . . . . . . . . . . . . . . . 281
12.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
12.6 Mathematica Commands in Text Format . . . . . . . . . . . . . 288
12.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
13 Complex Iterative Maps 293
13.1 Julia Sets and the Mandelbrot Set . . . . . . . . . . . . . . . . . 294
13.2 Boundaries of Periodic Orbits . . . . . . . . . . . . . . . . . . . 298
13.3 Mathematica Commands in Text Format . . . . . . . . . . . . . 300
13.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
viii Contents
14 ElectromagneticWaves and Optical Resonators 305
14.1 Maxwell抯 Equations and ElectromagneticWaves . . . . . . . . 306
14.2 Historical Background . . . . . . . . . . . . . . . . . . . . . . . 308
14.3 The Nonlinear SFR Resonator . . . . . . . . . . . . . . . . . . 312
14.4 Chaotic Attractors and Bistability . . . . . . . . . . . . . . . . . 314
14.5 Linear Stability Analysis . . . . . . . . . . . . . . . . . . . . . 318
14.6 Instabilities and Bistability . . . . . . . . . . . . . . . . . . . . 321
14.7 Mathematica Commands in Text Format . . . . . . . . . . . . . 325
14.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
15 Fractals and Multifractals 331
15.1 Construction of Simple Examples . . . . . . . . . . . . . . . . . 332
15.2 Calculating Fractal Dimensions . . . . . . . . . . . . . . . . . . 338
15.3 A Multifractal Formalism . . . . . . . . . . . . . . . . . . . . . 343
15.4 Multifractals in the RealWorld and Some Simple Examples . . . 348
15.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 356
15.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
16 Chaos Control and Synchronization 363
16.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . 364
16.2 Controlling Chaos in the Logistic Map . . . . . . . . . . . . . . 368
16.3 Controlling Chaos in the H閚on Map . . . . . . . . . . . . . . . 372
16.4 Chaos Synchronization . . . . . . . . . . . . . . . . . . . . . . 376
16.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 379
16.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
17 Neural Networks 387
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
17.2 The Delta Learning Rule and Backpropagation . . . . . . . . . . 394
17.3 The Hopfield Network and Lyapunov Stability . . . . . . . . . . 398
17.4 Neurodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 408
17.5 Mathematica Commands in Text Format . . . . . . . . . . . . . 411
17.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
18 Examination-Type Questions 421
18.1 Dynamical Systems with Applications . . . . . . . . . . . . . . 421
18.2 Dynamical Systems with Mathematica . . . . . . . . . . . . . . 424
19 Solutions to Exercises 429
19.0 Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
19.1 Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
19.2 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
19.3 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
19.4 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
Contents ix
19.5 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
19.6 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
19.7 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
19.8 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
19.9 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
19.10 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
19.11 Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
19.12 Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
19.13 Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
19.14 Chapter 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
19.15 Chapter 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
19.16 Chapter 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
19.17 Chapter 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
19.18 Chapter 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
References 451
Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
Research Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
Mathematica Program Index 469
Index 473
Dynamical Systems with Applications using MathematicaLy.part1
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Dynamical Systems with Applications using MathematicaLy.part2-4
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谢谢拉[m:01] [m:01] [m:01]
感谢分享
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感谢楼主分享
:11bb :11bb :11bb :11bb
后面的四个附件上传有问题，下载不下来，请楼主查看，谢谢！：15de
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谢谢楼主的分享啊。。。。。。。。。。
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找了好久才找到,希望能有所用!
many thanks!
谢谢楼主分享啊
动力学系统很复杂，特别是非线性现象的处理
非常感谢！！！！！！！！！！！！
不错的书，感谢分享，找了很久了
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thank you!!!!!!!!!!!!!!!!!!!
相当不错谢谢分享
好书，好人品！！！
Dynamical Systems with Applications using Mathematica: Dynamical Systems with Applications using MathematicaLy.part3.rar
