The nonlinear workbook : chaos, fractals, cellular automata, neural networks, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden Markov models, fuzzy logic with C++, Java and SymbolicC++ programs

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Başlık:

Yazar:

Steeb, W.-H.

ISBN:

9789812818539

9789812818522

Ek Yazar:

Steeb, W.-H.

Edition:

4th ed.

Yayım Bilgisi:

Fiziksel Tanım:

xix, 605 pages : illustrations ; 24 cm

Konu Terimleri:

Nonlinear programming.

Doğrusal olmayan programlama.

Nonlinear theories.

Doğrusal olmayan teoriler.

Added Author:

Hardy, Yorick, 1976-

Stoop, Ruedi.

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Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0097776	T57.8 S74 2008	Searching... Unknown

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Özet

New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 20 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 150 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, University of Johannesburg.

1 Nonlinear and Chaotic Maps	p. 1
1.1 One-Dimensional Maps	p. 1
1.1.1 Exact and Numerical Trajectories	p. 3
1.1.2 Fixed Points and Stability	p. 14
1.1.3 Invariant Density	p. 16
1.1.4 Liapunov Exponent	p. 20
1.1.5 Autocorrelation Function	p. 23
1.1.6 Discrete Fourier Transform	p. 25
1.1.7 Fast Fourier Transform	p. 28
1.1.8 Logistic Map and Liapunov Exponent for r [3,4]	p. 33
1.1.9 Logistic Map and Bifurcation Diagram	p. 34
1.1.10 Random Number Map and Invariant Density	p. 36
1.1.11 Random Number Map and Random Integration	p. 38
1.1.12 Circle Map and Rotation Number	p. 40
1.1.13 Newton Method	p. 41
1.1.14 Feigenbaum's Constant	p. 43
1.1.15 Symbolic Dynamics	p. 45
1.1.16 Chaotic Repeller	p. 47
1.1.17 Chaos and Encoding	p. 48
1.2 Two-Dimensional Maps	p. 54
1.2.1 Introduction	p. 54
1.2.2 Phase Portrait	p. 57
1.2.3 Fixed Points and Stability	p. 64
1.2.4 Liapunov Exponents	p. 65
1.2.5 Correlation Integral	p. 67
1.2.6 Capacity	p. 68
1.2.7 Hyperchaos	p. 70
1.2.8 Domain of Attraction	p. 74
1.2.9 Newton Method in the Complex Domain	p. 75
1.2.10 Newton Method in Higher Dimensions	p. 77
1.2.11 Ruelle-Takens-Newhouse Scenario	p. 78
1.2.12 Periodic Orbits and Topological Degree	p. 80
1.2.13 JPEG file	p. 82
2 Time Series Analysis	p. 85
2.1 Introduction	p. 85
2.2 Correlation Coefficient	p. 86
2.3 Liapunov Exponent from Time Series	p. 87
2.3.1 Jacobian Matrix Estimation Algorithm	p. 88
2.3.2 Direct Method	p. 89
2.4 Hurst Exponent	p. 96
2.4.1 Introduction	p. 96
2.4.2 Implementation for the Hurst Exponent	p. 98
2.4.3 Random Walk	p. 102
2.5 Higuchi's Algorithm	p. 106
2.6 Complexity	p. 107
3 Autonomous Systems in the Plane	p. 111
3.1 Classification of Fixed Points	p. 111
3.2 Homoclinic Orbit	p. 113
3.3 Pendulum	p. 114
3.4 Limit Cycle Systems	p. 116
3.5 Lotka-Volterra Systems	p. 119
4 Nonlinear Hamilton Systems	p. 123
4.1 Hamilton Equations of Motion	p. 123
4.1.1 Hamilton System and Variational Equation	p. 126
4.2 Integrable Hamilton Systems	p. 127
4.2.1 Hamilton Systems and First Integrals	p. 127
4.2.2 Lax Pair and Hamilton Systems	p. 128
4.2.3 Floquet Theory	p. 130
4.3 Chaotic Hamilton Systems	p. 133
4.3.1 Hénon-Heiles Hamilton Function and Trajectories	p. 133
4.3.2 Hénon Heiles and Surface of Section Method	p. 135
4.3.3 Quartic Potential and Surface of Section Technique	p. 136
5 Nonlinear Dissipative Systems	p. 139
5.1 Fixed Points and Stability	p. 139
5.2 Trajectories	p. 144
5.3 Phase Portrait	p. 148
5.4 Liapunov Exponents	p. 150
5.5 Generalized Lotka-Volterra Model	p. 153
5.6 Hyperchaotic Systems	p. 155
5.7 Hopf Bifurcation	p. 158
5.8 Time-Dependent First Integrals	p. 161
6 Nonlinear Driven Systems	p. 163
6.1 Introduction	p. 163
6.2 Driven Anharmonic Systems	p. 166
6.2.1 Phase Portrait	p. 166
6.2.2 Poincaré Section	p. 167
6.2.3 Liapunov Exponent	p. 169
6.2.4 Autocorrelation Function	p. 170
6.2.5 Power Spectral Density	p. 173
6.3 Driven Pendulum	p. 174
6.3.1 Phase Portrait	p. 174
6.3.2 Poincaré Section	p. 176
6.4 Parametrically Driven Pendulum	p. 178
6.4.1 Phase Portrait	p. 178
6.4.2 Poincaré Section	p. 179
6.5 Driven Van der Pol Equation	p. 181
6.5.1 Phase Portrait	p. 181
6.5.2 Liapunov Exponent	p. 183
6.6 Parametrically and Externally Driven Pendulum	p. 185
6.7 Torsion Numbers	p. 187
7 Controlling of Chaos	p. 191
7.1 Introduction	p. 191
7.2 Ott-Yorke-Grebogi Method	p. 191
7.2.1 One-Dimensional Maps	p. 191
7.2.2 Systems of Difference Equations	p. 195
7.3 Small Periodic Perturbation	p. 199
7.4 Resonant Perturbation and Control	p. 201
8 Synchronization of Chaos	p. 203
8.1 Introduction	p. 203
8.2 Synchronization of Chaos	p. 203
8.2.1 Synchronization Using Control	p. 203
8.2.2 Synchronizing Subsystems	p. 206
8.3 Synchronization of Coupled Dynamos	p. 209
8.4 Phase Coupled Systems	p. 211
9 Fractals	p. 217
9.1 Introduction	p. 217
9.2 Iterated Function System	p. 219
9.2.1 Introduction	p. 219
9.2.2 Cantor Set	p. 220
9.2.3 Heighway's Dragon	p. 223
9.2.4 Sierpinski Gasket	p. 225
9.2.5 Koch Curve	p. 227
9.2.6 Fern	p. 229
9.2.7 Grey Level Maps	p. 231
9.3 Mandelbrot Set	p. 232
9.4 Julia Set	p. 234
9.5 Fractals and Kronecker Product	p. 236
9.6 Lindenmayer Systems and Fractals	p. 240
9.7 Weierstrass Function	p. 243
10 Cellular Automata	p. 245
10.1 Introduction	p. 245
10.2 One-Dimensional Cellular Automata	p. 248
10.3 Sznajd Model	p. 249
10.4 Conservation Laws	p. 252
10.5 Two-Dimensional Cellular Automata	p. 253
10.6 Button Game	p. 257
11 Solving Differential Equations	p. 261
11.1 Introduction	p. 261
11.2 Euler Method	p. 262
11.3 Lie Series Technique	p. 264
11.4 Runge-Kutta-Fehlberg Technique	p. 268
11.5 Ghost Solutions	p. 269
11.6 Symplectic Integration	p. 272
11.7 Verlet Method	p. 277
11.8 Störmer Method	p. 279
11.9 Invisible Chaos	p. 280
11.10 First Integrals and Numerical Integration	p. 281
12 Neural Networks	p. 283
12.1 Introduction	p. 283
12.2 Hopfield Model	p. 287
12.2.1 Introduction	p. 287
12.2.2 Synchronous Operations	p. 289
12.2.3 Energy Function	p. 291
12.2.4 Basins and Radii of Attraction	p. 293
12.2.5 Spurious Attractors	p. 293
12.2.6 Hebb's Law	p. 294
12.2.7 Hopfield Example	p. 296
12.2.8 Hopfield C++ Program	p. 298
12.2.9 Asynchronous Operation	p. 302
12.2.10 Translation Invariant Pattern Recognition	p. 303
12.3 Similarity Metrics	p. 305
12.4 Kohonen Network	p. 309
12.4.1 Introduction	p. 309
12.4.2 Kohonen Algorithm	p. 310
12.4.3 Kohonen Example	p. 312
12.4.4 Traveling Salesman Problem	p. 318
12.5 Perceptron	p. 322
12.5.1 Introduction	p. 322
12.5.2 Boolean Functions	p. 324
12.5.3 Linearly Separable Sets	p. 325
12.5.4 Perceptron Learning	p. 326
12.5.5 Perceptron Learning Algorithm	p. 330
12.5.6 One and Two Layered Networks	p. 333
12.5.7 XOR Problem and Two-Layered Networks	p. 335
12.6 Multilayer Perceptrons	p. 339
12.6.1 Introduction	p. 339
12.6.2 Cybenko's Theorem	p. 340
12.6.3 Back-Propagation Algorithm	p. 340
12.6.4 Recursive Deterministic Perceptron Neural Networks	p. 348
12.7 Chaotic Neural Networks	p. 350
12.8 Neuronal-Oscillator Models	p. 351
12.9 Radial Basis Function Networks	p. 353
12.10 Neural Network, Matrices and Eigenvalues	p. 355
13 Genetic Algorithms	p. 357
13.1 Introduction	p. 357
13.2 Sequential Genetic Algorithm	p. 358
13.3 Schemata Theorem	p. 362
13.4 Bitwise Operations	p. 364
13.4.1 Introduction	p. 364
13.4.2 Assembly Language	p. 367
13.4.3 Floating Point Numbers and Bitwise Operations	p. 369
13.4.4 Java Bitset Class	p. 370
13.4.5 C++ Bitset Class	p. 371
13.5 Bit Vector Class	p. 373
13.6 Penna Bit-String Model	p. 376
13.7 Maximum of One-Dimensional Maps	p. 378
13.8 Maximum of Two-Dimensional Maps	p. 384
13.9 Finding a Fitness Function	p. 392
13.10 Problems with Constraints	p. 398
13.10.1 Introduction	p. 398
13.10.2 Knapsack Problem	p. 399
13.10.3 Traveling Salesman Problem	p. 404
13.11 Simulated Annealing	p. 412
14 Gene Expression Programming	p. 415
14.1 Introduction	p. 415
14.2 Example	p. 418
14.3 Numerical-Symbolic Manipulation	p. 430
14.4 Multi Expression Programming	p. 435
15 Optimization	p. 441
15.1 Lagrange Multiplier Method	p. 441
15.2 Karush-Kuhn-Tucker Conditions	p. 449
15.3 Support Vector Machine	p. 453
15.3.1 Introduction	p. 453
15.3.2 Linear Decision Boundaries	p. 453
15.3.3 Nonlinear Decision Boundaries	p. 457
15.3.4 Kernel Fisher Discriminant	p. 461
16 Discrete Wavelets	p. 465
16.1 Introduction	p. 465
16.2 Multiresolution Analysis	p. 468
16.3 Pyramid Algorithm	p. 470
16.4 Biorthogonal Wavelets	p. 475
16.5 Two-Dimensional Wavelets	p. 480
17 Discrete Hidden Markov Processes	p. 483
17.1 Introduction	p. 483
17.2 Markov Chains	p. 485
17.3 Discrete Hidden Markov Processes	p. 489
17.4 Forward-Backward Algorithm	p. 493
17.5 Viterbi Algorithm	p. 496
17.6 Baum-Welch Algorithm	p. 497
17.7 Distances between HMMs	p. 498
17.8 Application of HMMs	p. 499
17.9 C++ Program	p. 502
18 Fuzzy Sets and Fuzzy Logic	p. 513
18.1 Introduction	p. 513
18.2 Operators for Fuzzy Sets	p. 521
18.2.1 Logical Operators	p. 521
18.2.2 Algebraic Operators	p. 524
18.2.3 Defuzzification Operators	p. 525
18.2.4 Fuzzy Concepts as Fuzzy Sets	p. 527
18.2.5 Hedging	p. 528
18.2.6 Quantifying Fuzzyness	p. 529
18.2.7 C++ Implementation of Discrete Fuzzy Sets	p. 530
18.2.8 Applications: Simple Decision-Making Problems	p. 549
18.3 Fuzzy Numbers and Fuzzy Arithmetic	p. 555
18.3.1 Introduction	p. 555
18.3.2 Algebraic Operations	p. 556
18.3.3 LR-Representations	p. 559
18.3.4 Algebraic Operations on Fuzzy Numbers	p. 562
18.3.5 C++ Implementation of Fuzzy Numbers	p. 563
18.3.6 Applications	p. 570
18.4 Fuzzy Rule-Based Systems	p. 571
18.4.1 Introduction	p. 571
18.4.2 Fuzzy If-Then Rules	p. 574
18.4.3 Inverted Pendulum Control System	p. 575
18.4.4 Fuzzy Controllers with B-Spline Models	p. 577
18.4.5 Application	p. 580
18.5 Fuzzy C-Means Clustering	p. 582
18.6 fXOR Fuzzy Logic Networks	p. 586
18.7 Fuzzy Hamming Distance	p. 588
18.8 Fuzzy Truth Values and Probabilities	p. 591
Bibliography	p. 593
Index	p. 601

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