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The Nonlinear Workbook: Chaos, Fractals, Cellular Auromata, Neural Networks, Genetic Algorithms, Fuzzy Logic With C++, Java, Symbolicc++ and Reduce Programs book cover, ISBN 9789810240264

The Nonlinear Workbook: Chaos, Fractals, Cellular Auromata, Neural Networks, Genetic Algorithms, Fuzzy Logic With C++, Java, Symbolicc++ and Reduce Programs

by Steeb, Willi-Hans

ISBN13: 9789810240264
ISBN10: 9810240260
eBook ISBN(s): 9789814543491
Format: Paperback
Copyright: 1999-10-01
Publisher: WORLD SCIENTIFIC PUB CO INC

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1. The Nonlinear Workbook: Chaos, Fractals, Cellular Auromata, Neural Networks, Genetic Algorithms, Fuzzy Logic With C++, Java, Symbolicc++ and Reduce Programs > ISBN13: 9789810240264

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Summary

Willi-Hans Steeb is the Director of the International School for Scientific: Computing.

Table of Contents

Preface

v

Nonlinear and Chaotic Maps

1

(106)

One-Dimensional Maps

1

(66)

Exact and Numerical Trajectories

4

(17)

Fixed Points and Stability

21

(2)

Invariant Density

23

(7)

Liapunov Exponent

30

(5)

Autocorrelation Function

35

(3)

Discrete Fourier Transform

38

(4)

Fast Fourier Transform

42

(4)

Logistic Map and Liapunov Exponent for r ∈ [3, 4]

46

(2)

Logistic Map and Bifurcation Diagram

48

(3)

Random Number Map and Invariant Density

51

(3)

Random Number Map and Random Integration

54

(3)

Circle Map and Rotation Number

57

(2)

Newton Method

59

(3)

Feigenbaum's Constant

62

(2)

Symbolic Dynamics

64

(3)

Two-Dimensional Maps

67

(40)

Introduction

67

(2)

Phase Portrait

69

(14)

Fixed Points and Stability

83

(2)

Liapunov Exponents

85

(2)

Correlation Integral

87

(2)

Capacity

89

(3)

Hyperchaos

92

(5)

Domain of Attraction

97

(2)

Newton Method in the Complex domain

99

(3)

Newton Method in Higher Dimensions

102

(2)

Ruelle-Takens-Newhouse Scenario

104

(3)

Time Series Analysis

107

(28)

Introduction

107

(1)

Correlation Coefficient

108

(2)

Liapunov Exponent from Time Series

110

(12)

Jacobian Matrix Estimation Algorithm

111

(2)

Direct Method

113

(9)

Hurst Exponent

122

(8)

Introduction

122

(2)

Algorithm for the Hurst Exponent

124

(6)

Complexity

130

(5)

Autonomous Systems in the Plane

135

(18)

Classification of Fixed Points

135

(3)

Homoclinic Orbit

138

(3)

Pendulum

141

(3)

Limit Cycle Systems

144

(6)

Lotka-Volterra Systems

150

(3)

Nonlinear Hamilton Systems

153

(24)

Hamilton Equations of Motion

153

(6)

Hamilton System and Variational Equation

157

(2)

Integrable Hamilton Systems

159

(8)

Hamilton Systems and First Integrals

159

(2)

Lax Pair and Hamilton Systems

161

(4)

Floquet Theory

165

(2)

Chaotic Hamilton Systems

167

(10)

Henon-Heiles Hamilton Function and Trajectories

167

(3)

Henon-Heiles and Surface of Section method

170

(3)

Quartic Potential and Surface of Section Technique

173

(4)

Nonlinear Dissipative Systems

177

(28)

Fixed Points and Stability

177

(6)

Trajectories

183

(5)

Phase Portrait

188

(3)

Liapunov Exponents

191

(3)

Generalized Lotka-Volterra Model

194

(3)

Hyperchaotic Systems

197

(4)

Hopf Bifurcation

201

(2)

Time-Dependent First Integrals

203

(2)

Nonlinear Driven Systems

205

(38)

Introduction

205

(3)

Driven Anharmonic Systems

208

(14)

Phase Portrait

208

(2)

Poincare Section

210

(3)

Liapunov Exponent

213

(3)

Autocorrelation Function

216

(5)

Power Spectral Density

221

(1)

Driven Pendulum

222

(7)

Phase Portrait

222

(3)

Poincare Section

225

(4)

Parametrically Driven Pendulum

229

(4)

Phase Portrait

229

(2)

Poincare Section

231

(2)

Driven Van der Pol Equation

233

(6)

Phase Portrait

233

(4)

Liapunov Exponent

237

(2)

Parametrically and Externally Driven Pendulum

239

(4)

Controlling and Synchronization of Chaos

243

(32)

Introduction

243

(1)

Ott-Yorke-Grebogi Method

244

(10)

One-Dimensional Maps

244

(5)

Systems of Difference Equations

249

(5)

Small Periodic Perturbation

254

(4)

Resonant Perturbation and control

258

(1)

Synchronization of chaos

259

(9)

Synchronization Using Control

259

(4)

Synchronizing Subsystems

263

(5)

Phase Coupled Systems

268

(7)

Fractals

275

(24)

Introduction

275

(2)

Iterated Function System

277

(13)

Introduction

277

(1)

Cantor Set

278

(3)

Dragon

281

(3)

Sierpinski Gasket

284

(3)

Koch Curve

287

(3)

Mandelbrot Set

290

(3)

Julia Set

293

(3)

Weierstrass Function

296

(3)

Cellular Automata

299

(14)

Introduction

299

(3)

One-Dimensional Cellular Automata

302

(2)

Two-Dimensional Cellular Automata

304

(5)

Button Game

309

(4)

Solving Differential Equations

313

(24)

Introduction

313

(1)

Euler Method

314

(3)

Lie Series Technique

317

(5)

Runge-Kutta-Fehlberg Technique

322

(2)

Ghost Solutions

324

(5)

Symplectic Integration

329

(6)

Invisible Chaos

335

(2)

Neural Networks

337

(82)

Introduction

337

(5)

Hopfield Model

342

(24)

Introduction

342

(3)

Synchronous Operations

345

(3)

Energy Function

348

(2)

Basins and Radii of Attraction

350

(1)

Spurious Attractors

351

(1)

Hebb's Law

351

(3)

Example

354

(3)

Program

357

(6)

Asynchronous Operation

363

(1)

Translation Invariant Pattern Recognition

364

(2)

Similarity Metrics

366

(4)

Kohonen Network

370

(17)

Introduction

370

(1)

Algorithm

371

(3)

Example

374

(8)

Traveling Salesman Problem

382

(5)

Perceptron

387

(19)

Introduction

387

(3)

Boolean Functions

390

(1)

Linearly Separable Sets

391

(1)

Perceptron Learning

392

(3)

One- and Two-Layered Networks

395

(1)

Perceptron Learning Algorithm

396

(5)

The XOR Problem and Two-Layered Networks

401

(5)

Multilayer Perceptrons

406

(13)

Introduction

406

(1)

Cybenko's Theorem

407

(1)

Back-Propagation Algorithm

408

(11)

Genetic Algorithms

419

(76)

Introduction

419

(2)

The Sequential Genetic Alogrithm

421

(4)

Schemata Theorem

425

(3)

Bitwise Operations

428

(6)

A Bit Vector Class

434

(4)

Maximum of One-Dimensional Maps

438

(9)

Maximum of Two-Dimensional Maps

447

(11)

Problems with Constraints

458

(20)

Introduction

458

(2)

Knapsack Problem

460

(6)

Traveling Salesman Problem

466

(12)

Simulated Annealing

478

(3)

Parallel Genetic algorithms

481

(14)

Fuzzy Sets and Fuzzy Logic

495

(82)

Introduction

495

(7)

Operators for Fuzzy Sets

502

(44)

Logical Operators

502

(4)

Algebraic Operators

506

(2)

Defuzzifications Operators

508

(2)

Fuzzy Concepts as Fuzzy Sets

510

(2)

Hedging

512

(2)

Quantifying Fuzziness

514

(1)

C++ Implementation of Discrete Fuzzy Sets

515

(23)

Applications: Simple Decision-making Problems

538

(8)

Fuzzy Numbers and Fuzzy Arithmetic

546

(20)

Introduction

546

(1)

Algebraic Operations

547

(5)

LR-Representations

552

(3)

Algebraic Operations on Fuzzy Numbers

555

(2)

C++ Implementation of Fuzzy Numbers

557

(8)

Applications

565

(1)

Fuzzy Rule-Based Systems

566

(11)

Introduction

566

(5)

Fuzzy If-Then Rules

571

(1)

Inverted Pendulum Control System

572

(2)

Application

574

(3)

Bibliography

577

(6)

Index

583

Supplemental Materials

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