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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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
WS, World Scientific
2008
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 593 - 600 Literaturverz. S. 593 - 600 |
| Physical Description: | XIX, 605 S. |
| ISBN: | 9789812818539 9812818537 9789812818522 9812818529 |
Staff View
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV035338119 | ||
| 003 | DE-604 | ||
| 005 | 20090303 | ||
| 007 | t | ||
| 008 | 090227s2008 |||| 00||| eng d | ||
| 020 | |a 9789812818539 |c (pbk) US$58 / £31 |9 978-981-281-853-9 | ||
| 020 | |a 9812818537 |c (pbk) US$58 / £31 |9 981-281-853-7 | ||
| 020 | |a 9789812818522 |c hb US$98 / £53 |9 978-981-281-852-2 | ||
| 020 | |a 9812818529 |c hb US$98 / £53 |9 981-281-852-9 | ||
| 024 | 3 | |a 9789812818539 | |
| 035 | |a (OCoLC)234380356 | ||
| 035 | |a (DE-599)OBVAC06998896 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
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| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a ST 600 |0 (DE-625)143681: |2 rvk | ||
| 100 | 1 | |a Steeb, Willi-Hans |d 1945- |e Verfasser |0 (DE-588)12155614X |4 aut | |
| 245 | 1 | 0 | |a The nonlinear workbook |b 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 |c Willi-Hans Steeb. In collab. with Yorick Hardy ... |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b WS, World Scientific |c 2008 | |
| 300 | |a XIX, 605 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 593 - 600 | ||
| 500 | |a Literaturverz. S. 593 - 600 | ||
| 650 | 4 | |a Nonlinear programming | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Programmierung |0 (DE-588)4076370-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | 2 | |a Programmierung |0 (DE-588)4076370-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017142464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017142464 | ||
Record in the Search Index
| _version_ | 1804138653116530688 |
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| adam_text | Contents
1
Nonlinear and Chaotic Maps
1
1.1
One-Dimensional Maps
.......................... 1
1.1.1
Exact and Numerical Trajectories
................ 3
1.1.2
Fixed Points and Stability
.................... 14
1.1.3
Invariant Density
......................... 16
1.1.4
Liapunov Exponent
........................ 20
1.1.5
Autocorrelation Function
..................... 23
1.1.6
Discrete Fourier Transform
.................... 25
1.1.7
Fast Fourier Transform
...................... 28
1.1.8
Logistic Map and Liapunov Exponent for
r
Є
[3,4] ...... 33
1.1.9
Logistic Map and Bifurcation Diagram
............. 34
1.1.10
Random Number Map and Invariant Density
.......... 36
1.1.11
Random Number Map and Random Integration
........ 38
1.1.12
Circle Map and Rotation Number
................ 40
1.1.13
Newton Method
.......................... 41
1.1.14
Feigenbaum s Constant
...................... 43
1.1.15
Symbolic Dynamics
........................ 45
1.1.16
Chaotic
Repeller
......................... 47
1.1.17
Chaos and Encoding
....................... 48
1.2
Two-Dimensional Maps
.......................... 54
1.2.1
Introduction
............................ 54
1.2.2
Phase Portrait
........................... 57
1.2.3
Fixed Points and Stability
.................... 64
1.2.4
Liapunov Exponents
....................... 65
1.2.5
Correlation Integral
........................ 67
1.2.6
Capacity
.............................. 68
1.2.7
Hyperchaos
............................ 70
1.2.8
Domain of Attraction
....................... 74
1.2.9
Newton Method in the Complex Domain
............ 75
1.2.10
Newton Method in Higher Dimensions
............. 77
1.2.11
Ruelle-Takens-Newhouse Scenario
................ 78
1.2.12
Periodic Orbits and
Topologicei
Degree
............. 80
1.2.13
JPEG file
............................. 82
CONTENTS
Time Series Analysis
85
2.1
Introduction
................................85
2.2
Correlation Coefficient
..........................86
2.3
Liapunov Exponent from Time Series
..................87
2.3.1
Jacobian Matrix Estimation Algorithm
.............88
2.3.2
Direct Method
..........................89
2.4
Hurst Exponent
..............................96
2.4.1
Introduction
............................96
2.4.2
Implementation for the Hurst Exponent
............98
2.4.3
Random Walk
...........................102
2.5
Higuchi s Algorithm
............................106
2.6
Complexity
................................107
Autonomous Systems in the Plane 111
3.1
Classification of Fixed Points
......................
Ill
3.2
Homoclinic Orbit
.............................113
3.3
Pendulum
.................................114
3.4
Limit Cycle Systems
...........................116
3.5
Lotka-
Volterra Systems
..........................119
Nonlinear Hamilton Systems
123
4.1
Hamilton Equations of Motion
......................123
4.1.1
Hamilton System and Variational Equation
...........126
4.2
Integrable
Hamilton Systems
.......................127
4.2.1
Hamilton Systems and First Integrals
..............127
4.2.2
Lax Pair and Hamilton Systems
.................128
4.2.3
Floquet Theory
..........................130
4.3
Chaotic Hamilton Systems
........................133
4.3.1
Hénon-Heiles
Hamilton Function and Trajectories
.......133
4.3.2
Hénon
Heiles
and Surface of Section Method
..........135
4.3.3
Quartic Potential and Surface of Section Technique
......136
Nonlinear Dissipative Systems
139
5.1
Fixed Points and Stability
........................139
5.2
Trajectories
................................144
5.3
Phase Portrait
...............................148
5.4
Liapunov Exponents
...........................150
5.5
Generalized
Lotka-
Volterra Model
....................153
5.6
Hyperchaotic Systems
..........................155
5.7 Hopf
Bifurcation
.............................158
5.8
Time-Dependent First Integrals
.....................161
¡
Nonlinear Driven Systems
163
6.1
Introduction
................................163
6.2
Driven Anharmonic Systems
.......................166
CONTENTS xi
6.2.1 Phase
Portrait...........................
166
6.2.2
Poincaré Section
.........................167
6.2.3 Liapunov Exponent........................169
6.2.4
Autocorrelation Function
.....................170
6.2.5
Power Spectral Density
......................173
6.3
Driven Pendulum
.............................174
6.3.1
Phase Portrait
...........................174
6.3.2
Poincaré
Section
.........................176
6.4
Parametrically Driven Pendulum
....................178
6.4.1
Phase Portrait
...........................178
6.4.2
Poincaré
Section
.........................179
6.5
Driven Van
der Pol
Equation
......................181
6.5.1
Phase Portrait
...........................181
6.5.2
Liapunov Exponent
........................183
6.6
Parametrically and Externally Driven Pendulum
............185
6.7
Torsion Numbers
.............................187
7
Controlling of Chaos
191
7.1
Introduction
................................191
7.2
Ott-Yorke-Grebogi Method
........................191
7.2.1
One-Dimensional Maps
......................191
7.2.2
Systems of Difference Equations
.................195
7.3
Small Periodic Perturbation
.......................199
7.4
Resonant Perturbation and Control
...................201
8
Synchronization of Chaos
203
8.1
Introduction
................................203
8.2
Synchronization of Chaos
.........................203
8.2.1
Synchronization Using Control
..................203
8.2.2
Synchronizing Subsystems
....................206
8.3
Synchronization of Coupled Dynamos
..................209
8.4
Phase Coupled Systems
.........................211
9
Fractals 21T
9.1
Introduction
................................217
9.2
Iterated Function System
.........................219
9.2.1
Introduction
............................219
9.2.2
Cantor Set
.............................220
9.2.3
Heighway s Dragon
........................223
9.2.4
Sierpinski Gasket
.........................225
9.2.5
Koch Curve
............................227
9.2.6
Fern
................................229
9.2.7
Grey Level Maps
.........................231
9.3
Mandelbrot Set
..............................232
9.4
Julia Set
..................................234
xii CONTENTS
9.5
Fractals
and Kronecker
Product
.....................236
9.6 Lindenmayer
Systems and Fractals
...................240
9.7
Weierstrass
Function
...........................243
10
Cellular Automata
245
10.1
Introduction
................................245
10.2
One-Dimensional Cellular Automata
..................248
10.3
Sznajd Model
...............................249
10.4
Conservation Laws
............................252
10.5
Two-Dimensional Cellular Automata
..................253
10.6
Button Game
...............................257
11
Solving Differential Equations
261
11.1
Introduction
................................261
11.2
Euler
Method
...............................262
11.3
Lie Series Technique
...........................264
11.4
Runge-Kutta-Fehlberg Technique
....................268
11.5
Ghost Solutions
..............................269
11.6
Symplectic Integration
..........................272
11.7
Verlet
Method
...............................277
11.8
Störmer
Method
..............................279
11.9
Invisible Chaos
..............................280
ll.lOFirst Integrals and Numerical Integration
................281
12
Neural Networks
283
12.1
Introduction
................................283
12.2
Hopfield Model
..............................287
12.2.1
Introduction
............................287
12.2.2
Synchronous Operations
.....................289
12.2.3
Energy Function
.........................291
12.2.4
Basins and Radii of Attraction
..................293
12.2.5
Spurious Attractors
........................293
12.2.6
Hebb s Law
............................294
12.2.7
Hopfield Example
.........................296
12.2.8
Hopfield
C++
Program
.....................298
12.2.9
Asynchronous Operation
.....................302
12.2.10
Translation Invariant Pattern Recognition
...........303
12.3
Similarity Metrics
.............................305
12.4
Kohonen Network
.............................309
12.4.1
Introduction
............................309
12.4.2
Kohonen Algorithm
........................310
12.4.3
Kohonen Example
........................312
12.4.4
Traveling Salesman Problem
...................318
12.5
Perceptron
.................................322
12.5.1
Introduction
............................322
CONTENTS xiii
12.5.2
Boolean
Functions
........................324
12.5.3
Linearly Separable Sets
......................325
12.5.4
Perceptron Learning
.......................326
12.5.5
Perceptron Learning Algorithm
.................330
12.5.6
One and Two Layered Networks
.................333
12.5.7
XOR Problem and Two-Layered Networks
...........335
12.6
Multilayer Perceptrons
..........................339
12.6.1
Introduction
............................339
12.6.2
Cybenko s Theorem
........................340
12.6.3
Back-Propagation Algorithm
...................340
12.6.4
Recursive Deterministic Perceptron Neural Networks
......348
12.7
Chaotic Neural Networks
.........................350
12.8
Neuronal-Oscillator Models
.......................351
12.9
Radial Basis Function Networks
.....................353
^.lONeural Network, Matrices and Eigenvalues
...............355
13
Genetic Algorithms
357
13.1
Introduction
................................357
13.2
Sequential Genetic Algorithm
......................358
13.3
Schemata Theorem
............................362
13.4
Bitwise Operations
............................364
13.4.1
Introduction
............................364
13.4.2
Assembly Language
........................367
13.4.3
Floating Point Numbers and Bitwise Operations
........369
13.4.4
Java
Bitset
Class
.........................370
13.4.5 C++
bitset
Class
.........................371
13.5
Bit Vector Class
..............................373
13.6
Penna
Bit-String Model
.........................376
13.7
Maximum of One-Dimensional Maps
..................378
13.8
Maximum of Two-Dimensional Maps
..................384
13.9
Finding a Fitness Function
........................392
ІЗ.ЮРгоЬіегш
with Constraints
........................398
13.10.1
Introduction
............................398
13.10.2
Knapsack Problem
........................399
13.10.3
Traveling Salesman Problem
...................404
13.11Sinmlated
Annealing
...........................412
14
Gene Expression Programming
415
14.1
Introduction
................................415
14.2
Example
..................................418
14.3
Numerical-Symbolic Manipulation
....................430
14.4
Multi
Expression Programming
.....................435
CONTENTS
15
Optimization
15.1 Lagrange
Multiplier Method
.......................441
15.2
Karush-Kuhn-Tucker Conditions
.....................449
15.3
Support Vector Machine
.........................453
15.3.1
Introduction
............................453
15.3.2
Linear Decision Boundaries
...................453
15.3.3
Nonlinear Decision Boundaries
..................457
15.3.4
Kernel Fisher Discriminant
....................461
16
Discrete Wavelets
465
16.1
Introduction
................................465
16.2
Multiresolution Analysis
.........................468
16.3
Pyramid Algorithm
............................470
16.4 Biorthogonal
Wavelets
..........................475
16.5
Two-Dimensional Wavelets
........................480
17
Discrete Hidden Markov Processes
483
17.1
Introduction
................................483
17.2
Markov Chains
..............................485
17.3
Discrete Hidden Markov Processes
....................489
17.4
Forward-Backward Algorithm
......................493
17.5
Viterbi Algorithm
.............................496
17.6 Baum-
Welch Algorithm
..........................497
17.7
Distances between HMMs
........................498
17.8
Application of HMMs
...........................499
17.9 C++
Program
...............................502
18
Fuzzy Sets and Fuzzy Logic
513
18.1
Introduction
................................513
18.2
Operators for Fuzzy Sets
.........................521
18.2.1
Logical Operators
.........................521
18.2.2
Algebraic Operators
.......................524
18.2.3
Denazification Operators
....................525
18.2.4
Fuzzy Concepts as Fuzzy Sets
..................527
18.2.5
Hedging
..............................528
18.2.6
Quantifying Fuzzyness
......................529
18.2.7 C++
Implementation of Discrete Fuzzy Sets
..........530
18.2.8
Applications: Simple Decision-Making Problems
........549
18.3
Fuzzy Numbers and Fuzzy Arithmetic
.................555
18.3.1
Introduction
............................555
18.3.2
Algebraic Operations
.......................556
18.3.3
LR-Representations
........................559
18.3.4
Algebraic Operations on Fuzzy Numbers
............562
18.3.5 C++
Implementation of Fuzzy Numbers
............563
18.3.6
Applications
............................570
CONTENTS xv
18.4
Fuzzy Rule-Based Systems
........................571
18.4.1
Introduction
............................571
18.4.2
Fuzzy If-Then Rules
.......................574
18.4.3
Inverted Pendulum Control System
...............575
18.4.4
Fuzzy Controllers with B-Spline Models
............577
18.4.5
Application
............................580
18.5
Fuzzy
С
-Means Clustering
........................582
18.6
fXOR Fuzzy Logic Networks
.......................586
18.7
Fuzzy Hamming Distance
........................588
18.8
Fuzzy Truth Values and Probabilities
..................591
Bibliography
593
Index
601
|
| any_adam_object | 1 |
| author | Steeb, Willi-Hans 1945- |
| author_GND | (DE-588)12155614X |
| author_facet | Steeb, Willi-Hans 1945- |
| author_role | aut |
| author_sort | Steeb, Willi-Hans 1945- |
| author_variant | w h s whs |
| building | Verbundindex |
| bvnumber | BV035338119 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.8 |
| callnumber-search | T57.8 |
| callnumber-sort | T 257.8 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 810 SK 870 ST 600 |
| ctrlnum | (OCoLC)234380356 (DE-599)OBVAC06998896 |
| discipline | Informatik Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV035338119 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:31:36Z |
| institution | BVB |
| isbn | 9789812818539 9812818537 9789812818522 9812818529 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017142464 |
| oclc_num | 234380356 |
| open_access_boolean | |
| owner | DE-573 DE-20 DE-29T |
| owner_facet | DE-573 DE-20 DE-29T |
| physical | XIX, 605 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | WS, World Scientific |
| record_format | marc |
| spelling | Steeb, Willi-Hans 1945- Verfasser (DE-588)12155614X aut 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 Willi-Hans Steeb. In collab. with Yorick Hardy ... 4. ed. Singapore [u.a.] WS, World Scientific 2008 XIX, 605 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 593 - 600 Nonlinear programming Nonlinear theories Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Numerisches Verfahren (DE-588)4128130-5 s Programmierung (DE-588)4076370-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017142464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steeb, Willi-Hans 1945- 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 Nonlinear programming Nonlinear theories Numerisches Verfahren (DE-588)4128130-5 gnd Programmierung (DE-588)4076370-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4076370-5 (DE-588)4126142-2 |
| title | 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 |
| title_auth | 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 |
| title_exact_search | 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 |
| title_full | 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 Willi-Hans Steeb. In collab. with Yorick Hardy ... |
| title_fullStr | 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 Willi-Hans Steeb. In collab. with Yorick Hardy ... |
| title_full_unstemmed | 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 Willi-Hans Steeb. In collab. with Yorick Hardy ... |
| title_short | The nonlinear workbook |
| title_sort | 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 |
| title_sub | 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 |
| topic | Nonlinear programming Nonlinear theories Numerisches Verfahren (DE-588)4128130-5 gnd Programmierung (DE-588)4076370-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Nonlinear programming Nonlinear theories Numerisches Verfahren Programmierung Nichtlineares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017142464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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