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 Symbolic C++ Programs

by Steeb, Willi-Hans

• ISBN13: 9789812562913
• ISBN10: 9812562915
• eBook ISBN(s): 9789812567697, 9789813106482
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-07-15
• Publisher: World Scientific Pub Co Inc
• More Book Details
• Purchase Benefits

Table of Contents

Nonlinear and Chaotic Maps	1	(82)
One-Dimensional Maps	1	(52)
Exact and Numerical Trajectories	3	(12)
Fixed Points and Stability	15	(2)
Invariant Density	17	(5)
Liapunov Exponent	22	(4)
Autocorrelation Function	26	(2)
Discrete Fourier Transform	28	(2)
Fast Fourier Transform	30	(6)
Logistic Map and Liapunov Exponent for τ ε [3, 4]	36	(2)
Logistic Map and Bifurcation Diagram	38	(1)
Random Number Map and Invariant Density	39	(3)
Random Number Map and Random Integration	42	(2)
Circle Map and Rotation Number	44	(1)
Newton-Raphson Method	45	(2)
Feigenbaum's Constant	47	(2)
Symbolic Dynamics	49	(3)
Chaotic Repeller	52	(1)
Two-Dimensional Maps	53	(30)
Introduction	53	(1)
Phase Portrait	54	(9)
Fixed Points and Stability	63	(1)
Liapunov Exponents	64	(2)
Correlation Integral	66	(1)
Capacity	67	(3)
Hyperchaos	70	(4)
Domain of Attraction	74	(1)
Newton Method in the Complex Domain	75	(2)
Newton Method in Higher Dimensions	77	(2)
Ruelle-Takens-Newhouse Scenario	79	(2)
JPEG file	81	(2)
Time Series Analysis	83	(28)
Introduction	83	(1)
Correlation Coefficient	84	(1)
Liapunov Exponent from Time Series	85	(10)
Jacobian Matrix Estimation Algorithm	86	(2)
Direct Method	88	(7)
Hurst Exponent	95	(12)
Introduction	95	(3)
Implementation for the Hurst Exponent	98	(4)
Random Walk	102	(5)
Complexity	107	(4)
Autonomous Systems in the Plane	111	(13)
Classification of Fixed Points	111	(2)
Homoclinic Orbit	113	(1)
Pendulum	114	(2)
Limit Cycle Systems	116	(4)
Lotka-Volterra Systems	120	(4)
Nonlinear Hamilton Systems	124	(18)
Hamilton Equations of Motion	124	(4)
Hamilton System and Variational Equation	126	(2)
Integrable Hamilton Systems	128	(7)
Hamilton Systems and First Integrals	128	(1)
Lax Pair and Hamilton Systems	129	(3)
Floquet Theory	132	(3)
Chaotic Hamilton Systems	135	(7)
Henon-Heiles Hamilton Function and Trajectories	135	(2)
Henon Heiles and Surface of Section Method	137	(2)
Quartic Potential and Surface of Section Technique	139	(3)
Nonlinear Dissipative Systems	142	(26)
Fixed Points and Stability	142	(5)
Trajectories	147	(4)
Phase Portrait	151	(3)
Liapunov Exponents	154	(3)
Generalized Lotka-Volterra Model	157	(3)
Hyperchaotic Systems	160	(3)
Hopf Bifurcation	163	(3)
Time-Dependent First Integrals	166	(2)
Nonlinear Driven Systems	168	(29)
Introduction	168	(3)
Driven Anharmonic Systems	171	(9)
Phase Portrait	171	(1)
Poincare Section	172	(2)
Liapunov Exponent	174	(2)
Autocorrelation Function	176	(4)
Power Spectral Density	180	(1)
Driven Pendulum	180	(5)
Phase Portrait	180	(3)
Poincare Section	183	(2)
Parametrically Driven Pendulum	185	(3)
Phase Portrait	185	(2)
Poincare Section	187	(1)
Driven Van der Pol Equation	188	(5)
Phase Portrait	188	(3)
Liapunov Exponent	191	(2)
Parametrically and Externally Driven Pendulum	193	(4)
Controlling and Synchronization of Chaos	197	(25)
Introduction	197	(1)
Ott-Yorke-Grebogi Method	198	(8)
One-Dimensional Maps	198	(4)
Systems of Difference Equations	202	(4)
Small Periodic Perturbation	206	(3)
Resonant Perturbation and Control	209	(1)
Synchronization of Chaos	209	(7)
Synchronization Using Control	209	(3)
Synchronizing Subsystems	212	(4)
Phase Coupled Systems	216	(6)
Fractals	222	(22)
Introduction	222	(2)
Iterated Function System	224	(13)
Introduction	224	(1)
Cantor Set	225	(3)
Heighway's Dragon	228	(3)
Sierpinski Gasket	231	(1)
Koch Curve	232	(3)
Fern	235	(2)
Mandelbrot Set	237	(3)
Julia Set	240	(2)
Weierstrass Function	242	(2)
Cellular Automata	244	(13)
Introduction	244	(2)
One-Dimensional Cellular Automata	246	(2)
Two-Dimensional Cellular Automata	248	(5)
Button Game	253	(4)
Solving Differential Equations	257	(22)
Introduction	257	(1)
Euler Method	258	(1)
Lie Series Technique	259	(4)
Runge-Kutta-Fehlberg Technique	263	(1)
Ghost Solutions	264	(4)
Symplectic Integration	268	(5)
Verlet Method	273	(2)
Stormer Method	275	(1)
Invisible Chaos	276	(1)
First Integrals and Numerical Integration	277	(2)
Neural Networks	279	(71)
Introduction	279	(4)
Hopfield Model	283	(18)
Introduction	283	(2)
Synchronous Operations	285	(3)
Energy Function	288	(1)
Basins and Radii of Attraction	289	(1)
Spurious Attractors	290	(1)
Hebb's Law	290	(2)
Example	292	(2)
Program	294	(5)
Asynchronous Operation	299	(1)
Translation Invariant Pattern Recognition	300	(1)
Similarity Metrics	301	(5)
Kohonen Network	306	(13)
Introduction	306	(1)
Algorithm	307	(2)
Example	309	(6)
Traveling Salesman Problem	315	(4)
Perceptron	319	(18)
Introduction	319	(3)
Boolean Functions	322	(1)
Linearly Separable Sets	323	(1)
Perceptron Learning	324	(4)
One and Two Layered Networks	328	(1)
Perceptron Learning Algorithm	329	(3)
The XOR Problem and Two-Layered Networks	332	(5)
Multilayer Perceptrons	337	(11)
Introduction	337	(1)
Cybenko's Theorem	338	(1)
Back-Propagation Algorithm	339	(9)
Chaotic Neural Networks	348	(2)
Genetic Algorithms	350	(73)
Introduction	350	(1)
The Sequential Genetic Algorithm	351	(4)
Schemata Theorem	355	(2)
Bitwise Operations	357	(7)
A Bit Vector Class	364	(3)
Maximum of One-Dimensional Maps	367	(8)
Maximum of Two-Dimensional Maps	375	(9)
Finding a Fitness Function	384	(5)
Problems with Constraints	389	(17)
Introduction	389	(2)
Knapsack Problem	391	(6)
Traveling Salesman Problem	397	(9)
Simulated Annealing	406	(3)
Parallel Genetic Algorithms	409	(14)
Gene Expression Programming	423	(12)
Introduction	423	(3)
Example	426	(9)
Optimization	435	(18)
Lagrange Multiplier Method	435	(5)
Karush-Kuhn-Tucker Conditions	440	(4)
Support Vector Machine	444	(9)
Introduction	444	(1)
Linear Decision Boundaries	444	(4)
Nonlinear Decision Boundaries	448	(5)
Discrete Wavelets	453	(19)
Introduction	453	(2)
Multiresolution Analysis	455	(2)
Pyramid Algorithm	457	(6)
Biorthogonal Wavelets	463	(6)
Two-Dimensional Wavelets	469	(3)
Discrete Hidden Markov Processes	472	(30)
Introduction	472	(2)
Markov Chains	474	(4)
Discrete Hidden Markov Processes	478	(4)
Forward-Backward Algorithm	482	(3)
Viterbi Algorithm	485	(1)
Baum-Welch Algorithm	486	(1)
Distances between HMMs	487	(1)
Application of HMMs	488	(3)
Program	491	(11)
Fuzzy Sets and Fuzzy Logic	502	(75)
Introduction	502	(8)
Operators for Fuzzy Sets	510	(37)
Logical Operators	510	(3)
Algebraic Operators	513	(2)
Defuzzification Operators	515	(1)
Fuzzy Concepts as Fuzzy Sets	516	(2)
Hedging	518	(1)
Quantifying Fuzzyness	519	(1)
C++ Implementation of Discrete Fuzzy Sets	520	(20)
Applications: Simple Decision-Making Problems	540	(7)
Fuzzy Numbers and Fuzzy Arithmetic	547	(16)
Introduction	547	(1)
Algebraic Operations	548	(4)
LR-Representations	552	(2)
Algebraic Operations on Fuzzy Numbers	554	(2)
C++ Implementation of Fuzzy Numbers	556	(6)
Applications	562	(1)
Fuzzy Rule-Based Systems	563	(9)
Introduction	563	(4)
Fuzzy If-Then Rules	567	(1)
Inverted Pendulum Control System	568	(2)
Application	570	(2)
Fuzzy C-Means Clustering	572	(4)
Fuzzy Truth Values and Probabilities	576	(1)
Bibliography	577	(8)
Index	585