The nonlinear workbook: chaos, fractals, cellular automata, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden Markov models, fuzzy logic with C++, Java and SymbolicC++ programs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2011
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| Ausgabe: | 5. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 621 S. |
| ISBN: | 9789814335775 9814335770 9789814335782 9814335789 |
Internformat
MARC
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| 245 | 1 | 0 | |a The nonlinear workbook |b chaos, fractals, cellular automata, 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 5. ed. | ||
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Datensatz im Suchindex
| _version_ | 1804148805049778176 |
|---|---|
| adam_text | Titel: The nonlinear workbook
Autor: Steeb, Willi-Hans
Jahr: 2011
Contents
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................. 15
1.1.3 Invariant Density...................... 16
1.1.4 Liapunov Exponent..................... 21
1.1.5 Autocorrelation Function ................. 24
1.1.6 Discrete One-Dimensional Fourier Transform....... 26
1.1.7 Fast Fourier Transform................... 28
1.1.8 Logistic Map and Liapunov Exponent for r ? [3,4] ... 33
1.1.9 Logistic Map and Bifurcation Diagram.......... 34
1.1.10 Random Number Map and Invariant Density ...... 35
1.1.11 Random Number Map and Random Integration..... 38
1.1.12 Circle Map and Rotation Number............. 40
1.1.13 One-Dimensional Newton Method............. 41
1.1.14 Feigenbaum s Constant................... 44
1.1.15 Symbolic Dynamics..................... 45
1.1.16 Chaotic Repeller...................... 48
1.1.17 Chaos and Encoding.................... 48
1.1.18 Chaotic Data Communication............... 53
1.2 Two-Dimensional Maps........................ 57
1.2.1 Introduction......................... 57
1.2.2 Phase Portrait....................... 60
1.2.3 Fixed Points and Stability................. 67
1.2.4 Liapunov Exponents.................... 68
1.2.5 Correlation Integral .................... 70
1.2.6 Capacity........................... 71
1.2.7 Hyperchaos......................... 73
1.2.8 Domain of Attraction ................... 77
1.2.9 Newton Method in the Complex Domain......... 78
1.2.10 Newton Method in Higher Dimensions.......... 80
1.2.11 RueUe-Takens-Newhouse Scenario............. 81
1.2.12 Memikov Analysis for Maps................ 83
c CONTENTS
1.2.13 Periodic Orbits and Topological Degree..........84
1.2.14 JPEGfile..........................86
2 Time Series Analysis 89
2.1 Introduction..............................89
2.2 Correlation Coefficient........................90
2.3 Liapunov Exponent from Time Series................91
2.3.1 Jacobian Matrix Estimation Algorithm..........92
2.3.2 Direct Method.......................93
2.4 Hurst Exponent.............................99
2.4.1 Introduction.........................99
2.4.2 Implementation for the Hurst Exponent.........102
2.4.3 Random Walk........................106
2.5 Higuchi s Algorithm..........................110
2.6 Complexity ..............................110
3 Autonomous Systems in the Plane 115
3.1 Classification of Fixed Points.....................115
3.2 Homoclinic Orbit...........................117
3.3 One-Dimensional Pendulum.....................119
3.4 Limit Cycle Systems.........................120
3.5 Lotka-Volterra Systems........................124
4 Nonlinear Hamilton Systems 127
4.1 Hamilton Equations of Motion....................127
4.1.1 Hamilton System and Variational Equation.......130
4.2 Integrable Hamilton Systems.....................131
4.2.1 Hamilton Systems and First Integrals...........131
4.2.2 Lax Pak and Hamilton Systems..............134
4.2.3 Floquet Theory.......................136
4.3 Chaotic Hamilton Systems......................139
4.3.1 Trajectories and Henon-Heiles Hamilton Function .... 139
4.3.2 Surface of Section Method.................141
5 Nonlinear Dissipative Systems 147
5.1 Fixed Points and Stability......................147
5.2 Trajectories..............................152
5.3 Phase Portrait.............................156
5.4 Liapunov Exponents.........................159
5.5 Generalized Lotka-Volterra Model..................161
5.6 Hyperchaotic Systems.........................163
5.7 Hopf Bifurcation ...........................166
5.8 Time-Dependent First Integrals...................169
CONTENTS xi
6 Nonlinear Driven Systems 171
6.1 Introduction..............................171
6.2 Driven Anharmonic Systems.....................174
6.2.1 Phase Portrait.......................174
6.2.2 Poincare Section......................175
6.2.3 Liapunov Exponent.....................177
6.2.4 Autocorrelation Function .................178
6.2.5 Power Spectral Density ..................181
6.3 Driven Pendulum...........................182
6.3.1 Phase Portrait.......................182
6.3.2 Poincare Section......................184
6.4 Parametrically Driven Pendulum ..................186
6.4.1 Phase Portrait.......................186
6.4.2 Poincare Section......................187
6.5 Driven Van der Pol Equation.....................188
6.5.1 Phase Portrait.......................188
6.5.2 Liapunov Exponent.....................190
6.6 Parametrically and Externally Driven Pendulum..........192
6.7 Torsion Numbers...........................194
7 Controlling of Chaos 199
7.1 Introduction..............................199
7.2 Ott-Yorke-Grebogi Method......................199
7.2.1 One-Dimensional Maps...................199
7.2.2 Systems of Difference Equations..............203
7.3 Time-Delayed Feedback Control...................207
7.4 Small Periodic Perturbation.....................209
7.5 Resonant Perturbation and Control.................212
8 Synchronization of Chaos 213
8.1 Introduction..............................213
8.2 Synchronization of Chaos.......................213
8.2.1 Synchronization Using Control ..............213
8.2.2 Synchronizing Subsystems.................216
8.3 Synchronization of Coupled Dynamos................219
8.4 Phase Coupled Systems........................220
9 FractaLs 227
9.1 Introduction..............................227
9.2 Iterated Function System.......................229
9.2.1 Introduction.........................229
9.2.2 Cantor Set .........................230
9.2.3 Heighway s Dragon.....................233
9.2.4 Sierpinski Gasket......................235
9.2.5 Koch Curve.........................237
xii CONTENTS
9.2.6 Fern.............................239
9.2.7 Grey Level Maps......................241
9.3 Mandelbrot Set............................242
9.4 Julia Set................................244
9.5 Fractals and Kronecker Product...................246
9.6 Lindenmayer Systems and Fractals .................250
9.7 Weierstrass Function.........................253
9.8 Levy-Flight Random Walk......................255
10 Cellular Automata 257
10.1 Introduction..............................257
10.2 A Spin System and Cellular Automata...............260
10.3 Sznajd Model.............................261
10.4 Conservation Laws..........................264
10.5 Two-Dimensional Cellular Automata................265
10.6 Button Game.............................269
10.7 Langton s Ant.............................272
11 Solving Differential Equations 275
11.1 Introduction..............................275
11.2 Euler Method.............................276
11.3 Lie Series Technique .........................278
11.4 Runge-Kutta-Fehlberg Technique..................282
11.5 Ghost Solutions............................283
11.6 Symplectic Integration........................286
11.7 Verlet Method.............................291
11.8 Stornier Method............................292
11.9 Invisible Chaos............................293
11.10 First Integrals and Numerical Integration..............294
12 Optimization 297
12.1 Lagrange Multiplier Method.....................297
12.2 Coordinate Systems..........................302
12.3 Differential Forms...........................304
12.4 Karush-Kuhn-Tucker Conditions...................307
12.5 Support Vector Machine.......................311
12.5.1 Introduction.........................311
12.5.2 Linear Decision Boundaries................311
12.5.3 Nonlinear Decision Boundaries..............315
12.5.4 Kernel Fisher Discrimütant ................319
13 Neural Networks 323
13.1 Introduction..............................323
13.2 HopfieM Model............................327
13.2.1 Introduction.........................327
CONTENTS xiii
13.2.2 Synchronous Operations..................329
13.2.3 Energy Function......................331
13.2.4 Basins and Radii of Attraction..............332
13.2.5 Spurious Attractors.....................333
13.2.6 Hebb s Law.........................334
13.2.7 Hopfield Example......................335
13.2.8 Hopfield C++ Program..................337
13.2.9 Asynchronous Operation..................341
13.2.10 Translation Invariant Pattern Recognition........342
13.3 Similarity Metrics...........................344
13.4 Kohonen Network...........................348
13.4.1 Introduction.........................348
13.4.2 Kohonen Algorithm ....................349
13.4.3 Kohonen Example.....................351
13.4.4 Traveling Salesman Problem................357
13.5 Perceptron...............................360
13.5.1 Introduction.........................360
13.5.2 Boolean Functions.....................362
13.5.3 Linearly Separable Sets ..................363
13.5.4 Perceptron Learning....................364
13.5.5 Perceptron Learning Algorithm..............367
13.5.6 One and Two Layered Networks..............371
13.5.7 XOR Problem and Two-Layered Networks........372
13.6 Multilayer Perceptrons........................375
13.6.1 Introduction.........................375
13.6.2 Cybenko s Theorem ....................376
13.6.3 Back-Propagation Algorithm ...............377
13.7 Radial Basis Function Networks...................384
13.8 PERCEPTRON NEURAL NETWORKS..............387
13.9 Chaotic Neural Networks.......................389
13.10 Neuronal-Oscillator Models......................390
13.11 Neural Network, Matrices and Eigenvalues.............392
14 Genetic Algorithms 395
14.1 Introduction..............................395
14.2 Sequential Genetic Algorithm....................396
14.3 Schemata Theorem..........................400
14.4 Bitwise Operations..........................402
14.4.1 Introduction.........................402
14.4.2 Assembly Language....................405
14.4.3 Floating Point Numbers and Bitwise Operations.....407
14.4.4 Java Bitset Class......................408
14.4.5 C++ Bitset Class......................409
14.5 Bit Vector Class............................411
14.6 Penna Bit-String Model .......................414
xiv CONTENTS
14.7 Maximum of One-Dimensional Maps ................416
14.8 Maximum of Two-Dimensional Maps................421
14.9 Finding a Fitness Function......................428
14.10 Problems with Constraints......................435
14.10.1 Introduction.........................435
14.10.2 Knapsack Problem.....................436
14.10.3 Traveling Salesman Problem................441
14.11 Simulated Annealing.........................449
15 Gene Expression Programming 453
15.1 Introduction..............................453
15.2 Example................................456
15.3 Numerical-Symbolic Manipulation..................467
15.4 Multi Expression Programming...................472
16 Wavelets 479
16.1 Introduction..............................479
16.2 Multiresolution Analysis.......................482
16.3 Pyramid Algorithm and Discrete Wavelets.............485
16.4 Biorthogonal Wavelets........................489
16.5 Two-Dimensional Wavelets......................494
17 Discrete Hidden Markov Processes 497
17.1 Introduction..............................497
17.2 Markov Chams............................499
17.3 Discrete Hidden Markov Processes..................503
17.4 Forward-Backward Algorithm....................507
17.5 Viterbi Algorithm...........................510
17.6 Baum-Weich Algorithm........................511
17.7 Distances between Hidden Markov Models.............512
17.8 C++ Program.............................513
17.9 Application of Hidden Markov Models ...............521
18 Fuzzy Sets and Fuzzy Logic 525
18.1 Introduction..............................525
18.2 Operators for Fuzzy Sets.......................533
18.2.1 Logical Operators......................533
18.2.2 Algebraie Operators....................536
18.2.3 Defuzzification Operators.................538
18.2.4 Fuzzy Concepts as Fuzzy Sets...............539
18.2.5 Hedging............................540
18.2.6 Quantifying Fuzzyness...................542
18.2.7 C++ Implementation of Discrete Fuzzy Sets.......542
18.3 Fuzzy Numbers and Fuzzy Arithmetic................566
18.3.1 Introduction.........................566
CONTENTS xv
18.3.2 Algebraic Operations....................567
18.3.3 LR-Representations ....................570
18.3.4 Algebraic Operations on Fuzzy Numbers.........572
18.3.5 C++ Implementation of Fuzzy Numbers.........574
18.3.6 Applications.........................580
18.4 Fuzzy Rule-Based Systems......................580
18.4.1 Introduction.........................580
18.4.2 Fuzzy If-Then Rules....................584
18.4.3 Inverted Pendulum Control System............585
18.4.4 Fuzzy Controllers with B-Spline Models.........587
18.4.5 Application.........................589
18.5 Fuzzy C-Means Clustering......................591
18.6 T-Norms and T-Conorms.......................595
18.7 Fuzzy Logic Networks.........................597
18.8 Fuzzy Hamming Distance.......................599
18.9 Fuzzy Truth Values and Probabilities................602
Bibliography 603
Index 617
|
| any_adam_object | 1 |
| author | Steeb, Willi-Hans 1945- |
| author_GND | (DE-588)12155614X (DE-588)121556808 |
| author_facet | Steeb, Willi-Hans 1945- |
| author_role | aut |
| author_sort | Steeb, Willi-Hans 1945- |
| author_variant | w h s whs |
| building | Verbundindex |
| bvnumber | BV039865491 |
| 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)752255687 (DE-599)BVBBV039865491 |
| dewey-full | 519.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.76 |
| dewey-search | 519.76 |
| dewey-sort | 3519.76 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 5. ed. |
| format | Book |
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| id | DE-604.BV039865491 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:12:58Z |
| institution | BVB |
| isbn | 9789814335775 9814335770 9789814335782 9814335789 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024724950 |
| oclc_num | 752255687 |
| open_access_boolean | |
| owner | DE-29T DE-83 DE-634 |
| owner_facet | DE-29T DE-83 DE-634 |
| physical | XIX, 621 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Steeb, Willi-Hans 1945- Verfasser (DE-588)12155614X aut The nonlinear workbook chaos, fractals, cellular automata, 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 ... 5. ed. Singapore [u.a.] World Scientific 2011 XIX, 621 S. txt rdacontent n rdamedia nc rdacarrier Nonlinear programming Nonlinear theories Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Theorie (DE-588)4251279-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Programmierung (DE-588)4076370-5 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 Nichtlineare Optimierung (DE-588)4128192-5 s Nichtlineare Theorie (DE-588)4251279-7 s 1\p DE-604 Hardy, Yorick 1976- Sonstige (DE-588)121556808 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024724950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Steeb, Willi-Hans 1945- The nonlinear workbook chaos, fractals, cellular automata, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden Markov models, fuzzy logic with C++, Java and SymbolicC++ programs Nonlinear programming Nonlinear theories Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Programmierung (DE-588)4076370-5 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4128192-5 (DE-588)4251279-7 (DE-588)4128130-5 (DE-588)4076370-5 |
| title | The nonlinear workbook chaos, fractals, cellular automata, 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, 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, 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, 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, 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, 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 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, 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 Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Programmierung (DE-588)4076370-5 gnd |
| topic_facet | Nonlinear programming Nonlinear theories Nichtlineares dynamisches System Nichtlineare Optimierung Nichtlineare Theorie Numerisches Verfahren Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024724950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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