Nonlinear Workbook, The

Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Wavelets, Fuzzy Logic With C++, Java And Symbolic C++ Programs (2nd Edition)

By: Willi-hans Steeb

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Hardcover | 9 January 2003 | Edition Number 2

At a Glance

Hardcover
640 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 16.51 x 3.18

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The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 100 ready-to-run programs. The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing.

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Mathematics Applied Mathematics Nonlinear Science Mathematical Theory of Computation Maths for Computer Scientists Calculus & Mathematical Analysis Differential Calculus & Equations Optimisation

Linear Programming Booktopia Publisher Services World Scientific Publishing

Nonlinear and Chaotic Maps	p. 1
One-Dimensional Maps	p. 1
Exact and Numerical Trajectories	p. 4
Fixed Points and Stability	p. 21
Invariant Density	p. 23
Liapunov Exponent	p. 30
Autocorrelation Function	p. 35
Discrete Fourier Transform	p. 38
Fast Fourier Transform	p. 42
Logistic Map and Liapunov Exponent for [gamma] [set membership] [3, 4]	p. 49
Logistic Map and Bifurcation Diagram	p. 51
Random Number Map and Invariant Density	p. 53
Random Number Map and Random Integration	p. 56
Circle Map and Rotation Number	p. 59
Newton Method	p. 61
Feigenbaum's Constant	p. 64
Symbolic Dynamics	p. 66
Two-Dimensional Maps	p. 69
Introduction	p. 69
Phase Portrait	p. 71
Fixed Points and Stability	p. 82
Liapunov Exponents	p. 84
Correlation Integral	p. 86
Capacity	p. 88
Hyperchaos	p. 91
Domain of Attraction	p. 96
Newton Method in the Complex Domain	p. 98
Newton Method in Higher Dimensions	p. 101
Ruelle-Takens-Newhouse Scenario	p. 103
JPEG file	p. 106
Time Series Analysis	p. 109
Introduction	p. 109
Correlation Coefficient	p. 110
Liapunov Exponent from Time Series	p. 112
Jacobian Matrix Estimation Algorithm	p. 113
Direct Method	p. 115
Hurst Exponent	p. 125
Introduction	p. 125
Implementation for the Hurst Exponent	p. 128
Complexity	p. 134
Autonomous Systems in the Plane	p. 139
Classification of Fixed Points	p. 139
Homoclinic Orbit	p. 142
Pendulum	p. 144
Limit Cycle Systems	p. 146
Lotka-Volterra Systems	p. 151
Nonlinear Hamilton Systems	p. 155
Hamilton Equations of Motion	p. 155
Hamilton System and Variational Equation	p. 159
Integrable Hamilton Systems	p. 161
Hamilton Systems and First Integrals	p. 161
Lax Pair and Hamilton Systems	p. 163
Floquet Theory	p. 166
Chaotic Hamilton Systems	p. 171
Henon-Heiles Hamilton Function and Trajectories	p. 171
Henon Heiles and Surface of Section Method	p. 173
Quartic Potential and Surface of Section Technique	p. 176
Nonlinear Dissipative Systems	p. 179
Fixed Points and Stability	p. 179
Trajectories	p. 186
Phase Portrait	p. 191
Liapunov Exponents	p. 194
Generalized Lotka-Volterra Model	p. 198
Hyperchaotic Systems	p. 201
Hopf Bifurcation	p. 206
Time-Dependent First Integrals	p. 209
Nonlinear Driven Systems	p. 211
Introduction	p. 211
Driven Anharmonic Systems	p. 215
Phase Portrait	p. 215
Poincare Section	p. 217
Liapunov Exponent	p. 220
Autocorrelation Function	p. 223
Power Spectral Density	p. 228
Driven Pendulum	p. 229
Phase Portrait	p. 229
Poincare Section	p. 232
Parametrically Driven Pendulum	p. 235
Phase Portrait	p. 235
Poincare Section	p. 237
Driven Van der Pol Equation	p. 239
Phase Portrait	p. 239
Liapunov Exponent	p. 242
Parametrically and Externally Driven Pendulum	p. 245
Controlling and Synchronization of Chaos	p. 249
Introduction	p. 249
Ott-Yorke-Grebogi Method	p. 250
One-Dimensional Maps	p. 250
Systems of Difference Equations	p. 255
Small Periodic Perturbation	p. 260
Resonant Perturbation and Control	p. 263
Synchronization of Chaos	p. 264
Synchronization Using Control	p. 264
Synchronizing Subsystems	p. 268
Phase Coupled Systems	p. 272
Fractals	p. 279
Introduction	p. 279
Iterated Function System	p. 281
Introduction	p. 281
Cantor Set	p. 283
Heighway's Dragon	p. 286
Sierpinski Gasket	p. 289
Koch Curve	p. 291
Mandelbrot Set	p. 295
Julia Set	p. 298
Weierstrass Function	p. 300
Cellular Automata	p. 303
Introduction	p. 303
One-Dimensional Cellular Automata	p. 306
Two-Dimensional Cellular Automata	p. 308
Button Game	p. 313
Solving Differential Equations	p. 317
Introduction	p. 317
Euler Method	p. 318
Lie Series Technique	p. 320
Runge-Kutta-Fehlberg Technique	p. 325
Ghost Solutions	p. 327
Symplectic Integration	p. 332
Invisible Chaos	p. 338
Stormer Method	p. 340
Neural Networks	p. 341
Introduction	p. 341
Hopfield Model	p. 346
Introduction	p. 346
Synchronous Operations	p. 349
Energy Function	p. 352
Basins and Radii of Attraction	p. 354
Spurious Attractors	p. 355
Hebb's Law	p. 356
Example	p. 358
Program	p. 361
Asynchronous Operation	p. 367
Translation Invariant Pattern Recognition	p. 368
Similarity Metrics	p. 370
Kohonen Network	p. 376
Introduction	p. 376
Algorithm	p. 377
Example	p. 380
Traveling Salesman Problem	p. 388
Perceptron	p. 393
Introduction	p. 393
Boolean Functions	p. 396
Linearly Separable Sets	p. 398
Perceptron Learning	p. 399
One and Two Layered Networks	p. 403
Perceptron Learning Algorithm	p. 404
The XOR Problem and Two-Layered Networks	p. 409
Multilayer Perceptrons	p. 414
Introduction	p. 414
Cybenko's Theorem	p. 415
Back-Propagation Algorithm	p. 416
Genetic Algorithms	p. 427
Introduction	p. 427
The Sequential Genetic Algorithm	p. 429
Schemata Theorem	p. 433
Bitwise Operations	p. 436
A Bit Vector Class	p. 442
Maximum of One-Dimensional Maps	p. 446
Maximum of Two-Dimensional Maps	p. 455
Problems with Constraints	p. 465
Introduction	p. 465
Knapsack Problem	p. 468
Traveling Salesman Problem	p. 475
Simulated Annealing	p. 486
Parallel Genetic Algorithms	p. 489
Gene Expression Programming	p. 503
Introduction	p. 503
Example	p. 506
Discrete Wavelets	p. 515
Introduction	p. 515
Example	p. 520
Two-Dimensional Wavelets	p. 525
Fuzzy Sets and Fuzzy Logic	p. 527
Introduction	p. 527
Operators for Fuzzy Sets	p. 538
Logical Operators	p. 538
Algebraic Operators	p. 542
Defuzzification Operators	p. 544
Fuzzy Concepts as Fuzzy Sets	p. 546
Hedging	p. 548
Quantifying Fuzzyness	p. 550
C++ Implementation of Discrete Fuzzy Sets	p. 551
Applications: Simple Decision-Making Problems	p. 573
Fuzzy Numbers and Fuzzy Arithmetic	p. 581
Introduction	p. 581
Algebraic Operations	p. 582
LR-Representations	p. 587
Algebraic Operations on Fuzzy Numbers	p. 590
C++ Implementation of Fuzzy Numbers	p. 592
Applications	p. 600
Fuzzy Rule-Based Systems	p. 601
Introduction	p. 601
Fuzzy If-Then Rules	p. 606
Inverted Pendulum Control System	p. 607
Application	p. 609
Fuzzy Truth Values and Probabilities	p. 612
Bibliography	p. 613
Table of Contents provided by Ingram. All Rights Reserved.

Nonlinear Workbook, The

Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Wavelets, Fuzzy Logic With C++, Java And Symbolic C++ Programs (2nd Edition)

At a Glance

Hardcover

Shipping

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