| Nonlinear and Chaotic Maps | p. 1 |
| One-Dimensional Maps | p. 1 |
| Exact and Numerical Trajectories | p. 3 |
| Fixed Points and Stability | p. 14 |
| Invariant Density | p. 16 |
| Liapunov Exponent | p. 20 |
| Autocorrelation Function | p. 23 |
| Discrete Fourier Transform | p. 25 |
| 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. 36 |
| Random Number Map and Random Integration | p. 38 |
| Circle Map and Rotation Number | p. 40 |
| Newton Method | p. 41 |
| Feigenbaum's Constant | p. 43 |
| Symbolic Dynamics | p. 45 |
| Chaotic Repeller | p. 47 |
| Chaos and Encoding | p. 48 |
| Two-Dimensional Maps | p. 54 |
| Introduction | p. 54 |
| Phase Portrait | p. 57 |
| Fixed Points and Stability | p. 64 |
| Liapunov Exponents | p. 65 |
| Correlation Integral | p. 67 |
| Capacity | p. 68 |
| Hyperchaos | p. 70 |
| Domain of Attraction | p. 74 |
| Newton Method in the Complex Domain | p. 75 |
| Newton Method in Higher Dimensions | p. 77 |
| Ruelle-Takens-Newhouse Scenario | p. 78 |
| Periodic Orbits and Topological Degree | p. 80 |
| JPEG file | p. 82 |
| Time Series Analysis | p. 85 |
| Introduction | p. 85 |
| Correlation Coefficient | p. 86 |
| Liapunov Exponent from Time Series | p. 87 |
| Jacobian Matrix Estimation Algorithm | p. 88 |
| Direct Method | p. 89 |
| Hurst Exponent | p. 96 |
| Introduction | p. 96 |
| Implementation for the Hurst Exponent | p. 98 |
| Random Walk | p. 102 |
| Higuchi's Algorithm | p. 106 |
| Complexity | p. 107 |
| Autonomous Systems in the Plane | p. 111 |
| Classification of Fixed Points | p. 111 |
| Homoclinic Orbit | p. 113 |
| Pendulum | p. 114 |
| Limit Cycle Systems | p. 116 |
| Lotka-Volterra Systems | p. 119 |
| Nonlinear Hamilton Systems | p. 123 |
| Hamilton Equations of Motion | p. 123 |
| Hamilton System and Variational Equation | p. 126 |
| Integrable Hamilton Systems | p. 127 |
| Hamilton Systems and First Integrals | p. 127 |
| Lax Pair and Hamilton Systems | p. 128 |
| Floquet Theory | p. 130 |
| Chaotic Hamilton Systems | p. 133 |
| Hénon-Heiles Hamilton Function and Trajectories | p. 133 |
| Hénon Heiles and Surface of Section Method | p. 135 |
| Quartic Potential and Surface of Section Technique | p. 136 |
| Nonlinear Dissipative Systems | p. 139 |
| Fixed Points and Stability | p. 139 |
| Trajectories | p. 144 |
| Phase Portrait | p. 148 |
| Liapunov Exponents | p. 150 |
| Generalized Lotka-Volterra Model | p. 153 |
| Hyperchaotic Systems | p. 155 |
| Hopf Bifurcation | p. 158 |
| Time-Dependent First Integrals | p. 161 |
| Nonlinear Driven Systems | p. 163 |
| Introduction | p. 163 |
| Driven Anharmonic Systems | p. 166 |
| Phase Portrait | p. 166 |
| Poincaré Section | p. 167 |
| Liapunov Exponent | p. 169 |
| Autocorrelation Function | p. 170 |
| Power Spectral Density | p. 173 |
| Driven Pendulum | p. 174 |
| Phase Portrait | p. 174 |
| Poincaré Section | p. 176 |
| Parametrically Driven Pendulum | p. 178 |
| Phase Portrait | p. 178 |
| Poincaré Section | p. 179 |
| Driven Van der Pol Equation | p. 181 |
| Phase Portrait | p. 181 |
| Liapunov Exponent | p. 183 |
| Parametrically and Externally Driven Pendulum | p. 185 |
| Torsion Numbers | p. 187 |
| Controlling of Chaos | p. 191 |
| Introduction | p. 191 |
| Ott-Yorke-Grebogi Method | p. 191 |
| One-Dimensional Maps | p. 191 |
| Systems of Difference Equations | p. 195 |
| Small Periodic Perturbation | p. 199 |
| Resonant Perturbation and Control | p. 201 |
| Synchronization of Chaos | p. 203 |
| Introduction | p. 203 |
| Synchronization of Chaos | p. 203 |
| Synchronization Using Control | p. 203 |
| Synchronizing Subsystems | p. 206 |
| Synchronization of Coupled Dynamos | p. 209 |
| Phase Coupled Systems | p. 211 |
| Fractals | p. 217 |
| Introduction | p. 217 |
| Iterated Function System | p. 219 |
| Introduction | p. 219 |
| Cantor Set | p. 220 |
| Heighway's Dragon | p. 223 |
| Sierpinski Gasket | p. 225 |
| Koch Curve | p. 227 |
| Fern | p. 229 |
| Grey Level Maps | p. 231 |
| Mandelbrot Set | p. 232 |
| Julia Set | p. 234 |
| Fractals and Kronecker Product | p. 236 |
| Lindenmayer Systems and Fractals | p. 240 |
| Weierstrass Function | p. 243 |
| Cellular Automata | p. 245 |
| Introduction | p. 245 |
| One-Dimensional Cellular Automata | p. 248 |
| Sznajd Model | p. 249 |
| Conservation Laws | p. 252 |
| Two-Dimensional Cellular Automata | p. 253 |
| Button Game | p. 257 |
| Solving Differential Equations | p. 261 |
| Introduction | p. 261 |
| Euler Method | p. 262 |
| Lie Series Technique | p. 264 |
| Runge-Kutta-Fehlberg Technique | p. 268 |
| Ghost Solutions | p. 269 |
| Symplectic Integration | p. 272 |
| Verlet Method | p. 277 |
| Störmer Method | p. 279 |
| Invisible Chaos | p. 280 |
| First Integrals and Numerical Integration | p. 281 |
| Neural Networks | p. 283 |
| Introduction | p. 283 |
| Hopfield Model | p. 287 |
| Introduction | p. 287 |
| Synchronous Operations | p. 289 |
| Energy Function | p. 291 |
| Basins and Radii of Attraction | p. 293 |
| Spurious Attractors | p. 293 |
| Hebb's Law | p. 294 |
| Hopfield Example | p. 296 |
| Hopfield C++ Program | p. 298 |
| Asynchronous Operation | p. 302 |
| Translation Invariant Pattern Recognition | p. 303 |
| Similarity Metrics | p. 305 |
| Kohonen Network | p. 309 |
| Introduction | p. 309 |
| Kohonen Algorithm | p. 310 |
| Kohonen Example | p. 312 |
| Traveling Salesman Problem | p. 318 |
| Perceptron | p. 322 |
| Introduction | p. 322 |
| Boolean Functions | p. 324 |
| Linearly Separable Sets | p. 325 |
| Perceptron Learning | p. 326 |
| Perceptron Learning Algorithm | p. 330 |
| One and Two Layered Networks | p. 333 |
| XOR Problem and Two-Layered Networks | p. 335 |
| Multilayer Perceptrons | p. 339 |
| Introduction | p. 339 |
| Cybenko's Theorem | p. 340 |
| Back-Propagation Algorithm | p. 340 |
| Recursive Deterministic Perceptron Neural Networks | p. 348 |
| Chaotic Neural Networks | p. 350 |
| Neuronal-Oscillator Models | p. 351 |
| Radial Basis Function Networks | p. 353 |
| Neural Network, Matrices and Eigenvalues | p. 355 |
| Genetic Algorithms | p. 357 |
| Introduction | p. 357 |
| Sequential Genetic Algorithm | p. 358 |
| Schemata Theorem | p. 362 |
| Bitwise Operations | p. 364 |
| Introduction | p. 364 |
| Assembly Language | p. 367 |
| Floating Point Numbers and Bitwise Operations | p. 369 |
| Java Bitset Class | p. 370 |
| C++ Bitset Class | p. 371 |
| Bit Vector Class | p. 373 |
| Penna Bit-String Model | p. 376 |
| Maximum of One-Dimensional Maps | p. 378 |
| Maximum of Two-Dimensional Maps | p. 384 |
| Finding a Fitness Function | p. 392 |
| Problems with Constraints | p. 398 |
| Introduction | p. 398 |
| Knapsack Problem | p. 399 |
| Traveling Salesman Problem | p. 404 |
| Simulated Annealing | p. 412 |
| Gene Expression Programming | p. 415 |
| Introduction | p. 415 |
| Example | p. 418 |
| Numerical-Symbolic Manipulation | p. 430 |
| Multi Expression Programming | p. 435 |
| Optimization | p. 441 |
| Lagrange Multiplier Method | p. 441 |
| Karush-Kuhn-Tucker Conditions | p. 449 |
| Support Vector Machine | p. 453 |
| Introduction | p. 453 |
| Linear Decision Boundaries | p. 453 |
| Nonlinear Decision Boundaries | p. 457 |
| Kernel Fisher Discriminant | p. 461 |
| Discrete Wavelets | p. 465 |
| Introduction | p. 465 |
| Multiresolution Analysis | p. 468 |
| Pyramid Algorithm | p. 470 |
| Biorthogonal Wavelets | p. 475 |
| Two-Dimensional Wavelets | p. 480 |
| Discrete Hidden Markov Processes | p. 483 |
| Introduction | p. 483 |
| Markov Chains | p. 485 |
| Discrete Hidden Markov Processes | p. 489 |
| Forward-Backward Algorithm | p. 493 |
| Viterbi Algorithm | p. 496 |
| Baum-Welch Algorithm | p. 497 |
| Distances between HMMs | p. 498 |
| Application of HMMs | p. 499 |
| C++ Program | p. 502 |
| Fuzzy Sets and Fuzzy Logic | p. 513 |
| Introduction | p. 513 |
| Operators for Fuzzy Sets | p. 521 |
| Logical Operators | p. 521 |
| Algebraic Operators | p. 524 |
| Defuzzification Operators | p. 525 |
| Fuzzy Concepts as Fuzzy Sets | p. 527 |
| Hedging | p. 528 |
| Quantifying Fuzzyness | p. 529 |
| C++ Implementation of Discrete Fuzzy Sets | p. 530 |
| Applications: Simple Decision-Making Problems | p. 549 |
| Fuzzy Numbers and Fuzzy Arithmetic | p. 555 |
| Introduction | p. 555 |
| Algebraic Operations | p. 556 |
| LR-Representations | p. 559 |
| Algebraic Operations on Fuzzy Numbers | p. 562 |
| C++ Implementation of Fuzzy Numbers | p. 563 |
| Applications | p. 570 |
| Fuzzy Rule-Based Systems | p. 571 |
| Introduction | p. 571 |
| Fuzzy If-Then Rules | p. 574 |
| Inverted Pendulum Control System | p. 575 |
| Fuzzy Controllers with B-Spline Models | p. 577 |
| Application | p. 580 |
| Fuzzy C-Means Clustering | p. 582 |
| fXOR Fuzzy Logic Networks | p. 586 |
| Fuzzy Hamming Distance | p. 588 |
| Fuzzy Truth Values and Probabilities | p. 591 |
| Bibliography | p. 593 |
| Index | p. 601 |
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