Nonlinear Workbook, The

Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic With C++, Java And Symbolicc++ Programs (5th Edition)

By: Willi-hans Steeb

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Paperback | 18 March 2011 | Edition Number 5

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Paperback
642 Pages

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Revised

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22.86 x 15.24 x 3.28

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New Edition: The Nonlinear Workbook (6th Edition)The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 150 ready to run programs are included. New topics added to the fifth edition are Langton's ant, chaotic data communication, self-controlling feedback, differential forms and optimization, T-norms and T-conorms with applications.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Chaos Theory Optimisation Linear Programming Nonlinear Science Algebra Engineering & Technology Technology in General Science Physics

Booktopia Publisher Services World Scientific Publishing Calculus & Mathematical Analysis Complex Analysis

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Nonlinear and Chaotic Maps	p. 1
One-Dimensional Maps	p. 1
Exact and Numerical Trajectories	p. 3
Fixed Points and Stability	p. 15
Invariant Density	p. 16
Liapunov Exponent	p. 21
Autocorrelation Function	p. 24
Discrete One-Dimensional Fourier Transform	p. 26
Fast Fourier Transform	p. 28
Logistic Map and Liapunov Exponent for r ∈ [3, 4]	p. 33
Logistic Map and Bifurcation Diagram	p. 34
Random Number Map and Invariant Density	p. 35
Random Number Map and Random Integration	p. 38
Circle Map and Rotation Number	p. 40
One-Dimensional Newton Method	p. 41
Feigenbaum's Constant	p. 44
Symbolic Dynamics	p. 45
Chaotic Repeller	p. 48
Chaos and Encoding	p. 48
Chaotic Data Communication	p. 53
Two-Dimensional Maps	p. 57
Introduction	p. 57
Phase Portrait	p. 60
Fixed Points and Stability	p. 67
Liapunov Exponents	p. 68
Correlation Integral	p. 70
Capacity	p. 71
Hyperchaos	p. 73
Domain of Attraction	p. 77
Newton Method in the Complex Domain	p. 78
Newton Method in Higher Dimensions	p. 80
Ruelle-Takens-Newhouse Scenario	p. 81
Melnikov Analysis for Maps	p. 83
Periodic Orbits and Topological Degree	p. 84
JPEG file	p. 86
Time Series Analysis	p. 89
Introduction	p. 89
Correlation Coefficient	p. 90
Liapunov Exponent from Time Series	p. 91
Jacobian Matrix Estimation Algorithm	p. 92
Direct Method	p. 93
Hurst Exponent	p. 99
Introduction	p. 99
Implementation for the Hurst Exponent	p. 102
Random Walk	p. 106
Higuchi's Algorithm	p. 110
Complexity	p. 110
Autonomous Systems in the Plane	p. 115
Classification of Fixed Points	p. 115
Homoclinic Orbit	p. 117
One-Dimensional Pendulum	p. 119
Limit Cycle Systems	p. 120
Lotka-Volterra Systems	p. 124
Nonlinear Hamilton Systems	p. 127
Hamilton Equations of Motion	p. 127
Hamilton System and Variational Equation	p. 130
Integrable Hamilton Systems	p. 131
Hamilton Systems and First Integrals	p. 131
Lax Pair and Hamilton Systems	p. 134
Floquet Theory	p. 136
Chaotic Hamilton Systems	p. 139
Trajectories and Hénon-Heiles Hamilton Function	p. 139
Surface of Section Method	p. 141
Nonlinear Dissipative Systems	p. 147
Fixed Points and Stability	p. 147
Trajectories	p. 152
Phase Portrait	p. 156
Liapunov Exponents	p. 159
Generalized Lotka-Volterra Model	p. 161
Hyperchaotic Systems	p. 163
Hopf Bifurcation	p. 166
Time-Dependent First Integrals	p. 169
Nonlinear Driven Systems	p. 171
Introduction	p. 171
Driven Anharmonic Systems	p. 174
Phase Portrait	p. 174
Poincaré Section	p. 175
Liapunov Exponent	p. 177
Autocorrelation Function	p. 178
Power Spectral Density	p. 181
Driven Pendulum	p. 182
Phase Portrait	p. 182
Poincaré Section	p. 184
Parametrically Driven Pendulum	p. 186
Phase Portrait	p. 186
Poincaré Section	p. 187
Driven Van der Pol Equation	p. 188
Phase Portrait	p. 188
Liapunov Exponent	p. 190
Parametrically and Externally Driven Pendulum	p. 192
Torsion Numbers	p. 194
Controlling of Chaos	p. 199
Introduction	p. 199
Ott-Yorke-Grebogi Method	p. 199
One-Dimensional Maps	p. 199
Systems of Difference Equations	p. 203
Time-Delayed Feedback Control	p. 207
Small Periodic Perturbation	p. 209
Resonant Perturbation and Control	p. 212
Synchronization of Chaos	p. 213
Introduction	p. 213
Synchronization of Chaos	p. 213
Synchronization Using Control	p. 213
Synchronizing Subsystems	p. 216
Synchronization of Coupled Dynamos	p. 219
Phase Coupled Systems	p. 220
Fractals	p. 227
Introduction	p. 227
Iterated Function System	p. 229
Introduction	p. 229
Cantor Set	p. 230
Heighway's Dragon	p. 233
Sierpinski Gasket	p. 235
Koch Curve	p. 237
Fern	p. 239
Grey Level Maps	p. 241
Mandelbrot Set	p. 242
Julia Set	p. 244
Fractals and Kronecker Product	p. 246
Lindenmayer Systems and Fractals	p. 250
Weierstrass Function	p. 253
Lévy-Flight Random Walk	p. 255
Cellular Automata	p. 257
Introduction	p. 257
A Spin System and Cellular Automata	p. 260
Sznajd Model	p. 261
Conservation Laws	p. 264
Two-Dimensional Cellular Automata	p. 265
Button Game	p. 269
Langton's Ant	p. 272
Solving Differential Equations	p. 275
Introduction	p. 275
Euler Method	p. 276
Lie Series Technique	p. 278
Runge-Kutta-Fehlberg Technique	p. 282
Ghost Solutions	p. 283
Symplectic Integration	p. 286
Verlet Method	p. 291
Störmer Method	p. 292
Invisible Chaos	p. 293
First Integrals and Numerical Integration	p. 294
Optimization	p. 297
Lagrange Multiplier Method	p. 297
Coordinate Systems	p. 302
Differential Forms	p. 304
Karush-Kuhn-Tucker Conditions	p. 307
Support Vector Machine	p. 311
Introduction	p. 311
Linear Decision Boundaries	p. 311
Nonlinear Decision Boundaries	p. 315
Kernel Fisher Discriminant	p. 319
Neural Networks	p. 323
Introduction	p. 323
Hopfield Model	p. 327
Introduction	p. 327
Synchronous Operations	p. 329
Energy Function	p. 331
Basins and Radii of Attraction	p. 332
Spurious Attractors	p. 333
Hebb's Law	p. 334
Hopfield Example	p. 335
Hopfield C++ Program	p. 337
Asynchronous Operation	p. 341
Translation Invariant Pattern Recognition	p. 342
Similarity Metrics	p. 344
Kohonen Network	p. 348
Introduction	p. 348
Kohonen Algorithm	p. 349
Kohonen Example	p. 351
Traveling Salesman Problem	p. 357
Perceptron	p. 360
Introduction	p. 360
Boolean Functions	p. 362
Linearly Separable Sets	p. 363
Perceptron Learning	p. 364
Perceptron Learning Algorithm	p. 367
One and Two Layered Networks	p. 371
XOR Problem and Two-Layered Networks	p. 372
Multilayer Perceptrons	p. 375
Introduction	p. 375
Cybenko's Theorem	p. 376
Back-Propagation Algorithm	p. 377
Radial Basis Function Networks	p. 384
Perceptron Neural Networks	p. 387
Chaotic Neural Networks	p. 389
Neuronal-Oscillator Models	p. 390
Neural Network, Matrices and Eigenvalues	p. 392
Genetic Algorithms	p. 395
Introduction	p. 395
Sequential Genetic Algorithm	p. 396
Schemata Theorem	p. 400
Bitwise Operations	p. 402
Introduction	p. 402
Assembly Language	p. 405
Floating Point Numbers and Bitwise Operations	p. 407
Java Bitset Class	p. 408
C++ Bitset Class	p. 409
Bit Vector Class	p. 411
Penna Bit-String Model	p. 414
Maximum of One-Dimensional Maps	p. 416
Maximum of Two-Dimensional Maps	p. 421
Finding a Fitness Function	p. 428
Problems with Constraints	p. 435
Introduction	p. 435
Knapsack Problem	p. 436
Traveling Salesman Problem	p. 441
Simulated Annealing	p. 449
Gene Expression Programming	p. 453
Introduction	p. 453
Example	p. 456
Numerical-Symbolic Manipulation	p. 467
Multi Expression Programming	p. 472
Wavelets	p. 479
Introduction	p. 479
Multiresolution Analysis	p. 482
Pyramid Algorithm and Discrete Wavelets	p. 485
Biorthogonal Wavelets	p. 489
Two-Dimensional Wavelets	p. 494
Discrete Hidden Markov Processes	p. 497
Introduction	p. 497
Markov Chains	p. 499
Discrete Hidden Markov Processes	p. 503
Forward-Backward Algorithm	p. 507
Viterbi Algorithm	p. 510
Baum-Welch Algorithm	p. 511
Distances between Hidden Markov Models	p. 512
C++ Program	p. 513
Application of Hidden Markov Models	p. 521
Fuzzy Sets and Fuzzy Logic	p. 525
Introduction	p. 525
Operators for Fuzzy Sets	p. 533
Logical Operators	p. 533
Algebraic Operators	p. 536
Defuzzification Operators	p. 538
Fuzzy Concepts as Fuzzy Sets	p. 539
Hedging	p. 540
Quantifying Fuzzyness	p. 542
C++ Implementation of Discrete Fuzzy Sets	p. 542
Fuzzy Numbers and Fizzy Arithmetic	p. 566
Introduction	p. 566
Algebraic Operations	p. 567
LR-Representations	p. 570
Algebraic Operations on Fuzzy Numbers	p. 572
C++ Implementation of Fuzzy Numbers	p. 574
Applications	p. 580
Fuzzy Rule-Based Systems	p. 580
Introduction	p. 580
Fuzzy If-Then Rules	p. 584
Inverted Pendulum Control System	p. 585
Fuzzy Controllers with B-Spline Models	p. 587
Application	p. 589
Fuzzy C-Means Clustering	p. 591
T-Norms and T-Conorms	p. 595
Fuzzy Logic Networks	p. 597
Fuzzy Hamming Distance	p. 599
Fuzzy Truth Values and Probabilities	p. 602
Bibliography	p. 603
Index	p. 617
Table of Contents provided by Ingram. All Rights Reserved.

Nonlinear Workbook, The

Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic With C++, Java And Symbolicc++ Programs (5th Edition)

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

Hardcover

Hardcover

Hardcover

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