Dynamical systems with applications using MATLAB:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2004
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 459 S. graph. Darst. |
| ISBN: | 0817643214 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1821387851575590912 |
|---|---|
| adam_text |
STEPHEN LYNCH DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE XI 0 A TUTORIAL
INTRODUCTION TO MATLAB AND THE SYMBOLIC MATH TOOLBOX 1 0.1 TUTORIAL ONE:
THE BASICS AND THE SYMBOLIC MATH TOOLBOX (ONE HOUR) 2 0.2 TUTORIAL TWO:
PLOTS AND DIFFERENTIAL EQUATIONS (ONE HOUR) . 4 0.3 MATLAB PROGRAM
FILES, OR M-FILES 7 0.4 HINTS FOR PROGRAMMING 10 0.5 MATLAB EXERCISES .
. . '.-. 11 1 LINEAR DISCRETE DYNAMICAL SYSTEMS 15 1.1 RECURRENCE
RELATIONS 16 1.2 THE LESLIE MODEL 21 1.3 HARVESTING AND CULLING POLICIES
25 1.4 MATLAB COMMANDS 30 1.5 EXERCISES 30 2 NONLINEAR DISCRETE
DYNAMICAL SYSTEMS 35 2. 1 THE TENT MAP AND GRAPHICAL ITERATIONS 36 2.2
FIXED POINTS AND PERIODIC ORBITS 40 2.3 THE LOGISTIC MAP, BIFURCATION
DIAGRAM, AND FEIGENBAUM NUMBER 48 2.4 GAUSSIAN AND HENON MAPS 55 VI
CONTENTS 2.5 APPLICATIONS 59 2.6 MATLAB COMMANDS 62 2.7 EXERCISES 66 3
COMPLEX ITERATIVE MAPS 69 3.1 JULIA SETS AND THE MANDELBROT SET 70 3.2
BOUNDARIES OF PERIODIC ORBITS 74 3.3 MATLAB COMMANDS 76 3.4 EXERCISES 79
4 ELECTROMAGNETIC WAVES AND OPTICAL RESONATORS 81 4.1 MAXWELL'S
EQUATIONS AND ELECTROMAGNETIC WAVES 82 4.2 HISTORICAL BACKGROUND 84 4.3
THE NONLINEAR SFR RESONATOR 89 4.4 CHAOTIC ATTRACTORS AND BISTABILITY 91
4.5 LINEAR STABILITY ANALYSIS 94 4.6 INSTABILITIES AND BISTABILITY 97
4.7 MATLAB COMMANDS 101 4.8 EXERCISES 104 5 FRACTALS AND MULTIFRACTALS
109 5.1 CONSTRUCTION OF SIMPLE EXAMPLES 110 5.2 CALCULATING FRACTAL
DIMENSIONS 116 5.3 A MULTIFRACTAL FORMALISM 121 5.4 MULTIFRACTALS IN THE
REAL WORLD AND SOME SIMPLE EXAMPLES . . . 126 5.5 MATLAB COMMANDS 133
5.6 EXERCISES 137 6 CONTROLLING CHAOS 143 6.1 HISTORICAL BACKGROUND 144
6.2 CONTROLLING CHAOS IN THE LOGISTIC MAP 148 6.3 CONTROLLING CHAOS IN
THE HENON MAP 151 6.4 MATLAB COMMANDS 155 6.5 EXERCISES 157 7
DIFFERENTIAL EQUATIONS 161 7.1 SIMPLE DIFFERENTIAL EQUATIONS AND
APPLICATIONS 162 7.2 APPLICATIONS TO CHEMICAL KINETICS 169 7.3
APPLICATIONS TO ELECTRIC CIRCUITS 172 7.4 EXISTENCE AND UNIQUENESS
THEOREM 176 7.5 MATLAB COMMANDS 179 7.6 EXERCISES 180 CONTENTS VII 8
PLANAR SYSTEMS 185 8.1 CANONICAL FORMS 186 8.2 EIGENVECTORS DENNING
STABLE AND UNSTABLE MANIFOLDS 190 8.3 PHASE PORTRAITS OF LINEAR SYSTEMS
IN THE PLANE 193 8.4 LINEARIZATION AND HARTMAN'S THEOREM 197 8.5
CONSTRUCTING PHASE PLANE DIAGRAMS 199 8.6 MATLAB COMMANDS 208 8.7.
EXERCISES 210 9 INTERACTING SPECIES 215 9.1 COMPETING SPECIES 215 9.2
PREDATOR-PREY MODELS 218 9.3 OTHER CHARACTERISTICS AFFECTING INTERACTING
SPECIES 224 9.4 MATLAB COMMANDS 225 9.5 EXERCISES 226 10 LIMIT CYCLES
229 10.1 HISTORICAL BACKGROUND 229 10.2 EXISTENCE AND UNIQUENESS OF
LIMIT CYCLES IN THE PLANE 232 10.3 NONEXISTENCE OF LIMIT CYCLES IN THE
PLANE 237 10.4 EXERCISES 241 11 HAMILTONIAN SYSTEMS, LYAPUNOV FUNCTIONS,
AND STABILITY 243 11.1 HAMILTONIAN SYSTEMS IN THE PLANE 244 11.2
LYAPUNOV FUNCTIONS AND STABILITY 249 11.3 EXERCISES 253 12 BIFURCATION
THEORY 257 12.1 BIFURCATIONS OF NONLINEAR SYSTEMS IN THE PLANE 258 12.2
MULTISTABILITY AND BISTABILITY 264 12.3 MATLAB COMMANDS . I 267 12.4
EXERCISES 268 13 THREE-DIMENSIONAL AUTONOMOUS SYSTEMS AND CHAOS 271 13.1
LINEAR SYSTEMS AND CANONICAL FORMS 272 13.2 NONLINEAR SYSTEMS AND
STABILITY 276 13.3 THE ROSSLER SYSTEM AND CHAOS 280 13.4 THE LORENZ
EQUATIONS, CHUA'S CIRCUIT, AND THE BELOUSOV-ZHABOTINSKI REACTION 284
13.5 MATLAB COMMANDS 291 13.6 EXERCISES 292 14 POINCARE MAPS AND
NONAUTONOMOUS SYSTEMS IN THE PLANE 297 14.1 POINCARE MAPS 298 VIII
CONTENTS 14.2 HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM 304 14.3
NONAUTONOMOUS SYSTEMS IN THE PLANE 307 14.4 MATLAB COMMANDS 316 14.5
EXERCISES 320 15 LOCAL AND GLOBAL BIFURCATIONS 323 15.1 SMALL-AMPLITUDE
LIMIT CYCLE BIFURCATIONS . . . 324 15.2 MELNIKOV INTEGRALS AND
BIFURCATING LIMIT CYCLES FROM A CENTER . 328 15.3 HOMOCLINIC
BIFURCATIONS 330 15.4 MATLAB COMMANDS 332 15.5 EXERCISES 332 16 THE
SECOND PART OF HUBERT'S SIXTEENTH PROBLEM 335 16.1 STATEMENT OF PROBLEM
AND MAIN RESULTS 336 16.2 POINCARE" COMPACTIFICATION 338 16.3 GLOBAL
RESULTS FOR LIENARD SYSTEMS 345 16.4 LOCAL RESULTS FOR LIENARD SYSTEMS
352 16.5 EXERCISES 354 17 NEURAL NETWORKS 359 17.1 INTRODUCTION 360 17.2
THE DELTA LEARNING RULE AND BACKPROPAGATION 366 17.3 THE HOPFIELD
NETWORK AND LYAPUNOV STABILITY 370 17.4 NEURODYNAMICS 379 17.5 MATLAB
COMMANDS 383 17.6 EXERCISES 391 18 SIMULINK 397 18.1 INTRODUCTION 398
18.2 ELECTRIC CIRCUITS 401 18.3 A MECHANICAL SYSTEM 402 18.4 NONLINEAR
OPTICS 403 18.5 THE LORENZ EQUATIONS AND CHAOS SYNCHRONIZATION 405 18.6
EXERCISES 405 19 SOLUTIONS TO EXERCISES 409 19.0 CHAPTER 0 409 19.1
CHAPTER 1 411 19.2 CHAPTER 2 412 19.3 CHAPTER 3 413 19.4 CHAPTER 4 414
19.5 CHAPTER 5 415 19.6 CHAPTER 6 416 19.7 CHAPTER7 416 CONTENTS IX 19.8
CHAPTER 8 417 19.9 CHAPTER 9 419 19.10 CHAPTER 10 420 19.11 CHAPTER 11
422 19.12 CHAPTER 12 422 19.13 CHAPTER 13 424 19.14 CHAPTER 14 425 19.15
CHAPTER 15 426 19.16 CHAPTER 16 426 19.17 CHAPTER 17 427 19.18 CHAPTER
18 428 REFERENCES 429 TEXTBOOKS 429 RESEARCH PAPERS 434 MATLAB PROGRAM
FILE INDEX 443 SIMULINK MODEL FILE INDEX 447 INDEX 449 |
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| spelling | Lynch, Stephen 1964- Verfasser (DE-588)122765052 aut Dynamical systems with applications using MATLAB Stephen Lynch Boston [u.a.] Birkhäuser 2004 XV, 459 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier MATLAB Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s MATLAB (DE-588)4329066-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012887826&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lynch, Stephen 1964- Dynamical systems with applications using MATLAB MATLAB Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4329066-8 |
| title | Dynamical systems with applications using MATLAB |
| title_auth | Dynamical systems with applications using MATLAB |
| title_exact_search | Dynamical systems with applications using MATLAB |
| title_full | Dynamical systems with applications using MATLAB Stephen Lynch |
| title_fullStr | Dynamical systems with applications using MATLAB Stephen Lynch |
| title_full_unstemmed | Dynamical systems with applications using MATLAB Stephen Lynch |
| title_short | Dynamical systems with applications using MATLAB |
| title_sort | dynamical systems with applications using matlab |
| topic | MATLAB Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System |
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