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9789812562913

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
  • ISBN13:

    9789812562913

  • ISBN10:

    9812562915

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2005-07-15
  • Publisher: World Scientific Pub Co Inc
  • Purchase Benefits
List Price: $55.00
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    $63.00
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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

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