From equilibrium to chaos: practical bifurcation and stability analysis
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Elsevier
1988
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 339 - 358. - 2. Aufl. u.d.T.: Practical bifurcation and stability analysis |
| Physical Description: | XV, 367 S. graph. Darst. |
| ISBN: | 0444012508 |
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Record in the Search Index
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| adam_text | FROM EQUILIBRIUM TO CHAOS PRACTICA! BIFURCATION AND STABILITY ANALYSIS
RUEDIGER SEYDEL INSTITUT FUER ANGEWANDTE MATHEMATIK UND STATISTIK
UNIVERSITY OF WUERZBURG WUERZBURG, FEDERAL REPUBLIC OF GERMANY ELSEVIER
NEW YORK * AMSTERDAM * LONDON CONTENTS PREFACE IX NOTATION XUEI 1
INTRODUCTION AND PREREQUISITES 1 1.1 A NONMATHEMATICAL INTRODUCTION 1
1.2 FUNDAMENTALS OF STATIONARY POINTS AND STABILITY (ODES) 4 1.2.1
TRAJECTORIES AND EQUILIBRIA 4 1.2.2 DEVIATIONS 6 1.2.3 STABILITY 8 1.2.4
LINEAR STABILITY; DUFFING EQUATION 10 1.2.5 DEGENERATE CASES, PARAMETER
DEPENDENCE 18 1.2.6 GENERALIZATIONS 20 1.3 FUNDAMENTALS OF LIMIT CYCLES
AND WAVES 21 1.3.1 VAN DER POL EQUATION 22 1.3.2 WAVES 25 1.4 SOME
FUNDAMENTAL NUMERICAL METHODS 29 2 BASIC NONLINEAR PHENOMENA 35 2.1 A
PREPARATORY EXAMPLE 35 2.2 ELEMENTARY DEFINITIONS 38 2.3 BUECKLING AND
OSCILLATION OF A BEAM 40 2.4 TURNING POINTS AND BIFURCATION POINTS: THE
GEOMETRIE VIEW 44 2.5 TUMING POINTS AND BIFURCATION POINTS: THE
ALGEBRAIC VIEW 52 ; III IV CONTENTS 2.6 HOPF BIFURCATION 60 2.7
CONVECTION DESCRIBED BY LORENZ S EQUATION 66 2.8 HOPF BIFURCATION AND
STABILITY 71 2.9 GENERIC BRANCHING 78 2.10 BIFURCATION IN THE PRESENCE
OF SYMMETRY 91 3 PRACTICAL PROBLEMS 93 3.1 READILY AVAILABLE TOOLS AND
LIMITED RESULTS 93 3.2 PRINCIPAL TASKS 94 3.3 WHAT ELSE CAN HAPPEN 97
3.4 MARANGONI CONVECTION 101 3.5 THE ART AND SCIENCE OF PARAMETER STUDY
106 4 PRINCIPLES OF CONTINUATION 109 4.1 PREDICTORS 111 4.1.1
ODE-METHODS; TANGENT PREDICTOR 111 4.1.2 POLYNOMIAL EXTRAPOLATION;
SECANT PREDICTOR 113 4.2 PARAMETERIZATIONS 114 4.2.1 PARAMETERIZATION BY
ADDING AN EQUATION 114 4.2.2 ARCLENGTH AND PSEUDO ARCLENGTH 776 4.2.3
LOCAL PARAMETERIZATION 776 4.3 CORRECTORS 779 4.4 STEP CONTROLS 122 4.5
CONTINUATION SUBJECT TO CONSTRAINTS 724 4.6 MORE PRACTICAL ASPECTS 125 5
CALCULATION OF THE BRANCHING BEHAVIOR OF NONLINEAR EQUATIONS 729 5.1
CALCULATING STABILITY 729 5.2 BRANCHING TEST FUNCTIONS 732 5.3 GENERAL
METHODS FOR CALCULATING BRANCH POINTS 737 5.3.1 INDIRECT METHODS 737
5.3.2 DIRECT METHODS 744 5.3.3 AN ELECTRICAL CIRCUIT 750 5.3.4 A FAMILY
OF TEST FUNCTIONS 154 5.3.5 TEMPERATURE DISTRIBUTION IN A REACTING
MATERIAL 157 5.3.6 DIRECT VERSUS INDIRECT METHODS 161 5.4 BRANCH
SWITCHING 162 5.4.1 CONSTRUCTING A PREDICTOR VIA THE TANGENT 163 5.4.2
PREDICTORS BASED ON INTERPOLATION 166 5.4.3 CORRECTORS WITH SELECTIVE
PROPERTIES 169 5.4.4 SYMMETRY BREAKING 172 5.4.5 COUPLED CELL REACTION
173 5.4.6 PARAMETERIZATION BY IRREGULARITY 178 5.4.7 OTHER METHODS 179
5.5 METHODS FOR CALCULATING SPECIFIC BRANCH POINTS 182 5.5.1 A SPECIAL
IMPLEMENTATION FOR THE BRANCHING SYSTEM 183 5.5.2 REGULAER SYSTEMS FOR
BIFURCATION POINTS 186 5.5.3 METHODS FOR TURNING POINTS 187 5.5.4
METHODS FOR HOPF BIFURCATION POINTS 187 5.5.5 OTHER METHODS 189 5.6
CONCLUDING REMARKS 189 5.7 TWO-PARAMETER PROBLEMS 190 6 CALCULATING
BRANCHING BEHAVIOR OF ODE BOUNDARY-VALUE PROBLEMS 195 6.1 ENLARGED
BOUNDARY-VALUE PROBLEMS 196 6.2 CALCULATION OF BRANCH POINTS 206 6.2.1
BRANCHING SYSTEM 206 6.2.2 CATALYTIC REACTION 207 6.2.3 INITIAL
APPROXIMATION AND BRANCHING TEST FUNCTION 209 6.3 STEPPING DOWN FOR AN
IMPLEMENTATION 211 6.4 BRANCH SWITCHING AND SYMMETRY 213 6.5 TRIVIAL
BIFURCATION 222 6.6 TESTING STABILITY 226 6.7 HOPF BIFURCATION IN PDES
229 VI CONTENTS 7 STABILITY OF PERIODIC SOLUTIONS 235 7.1 PERIODIC
SOLUTIONS OF AUTONOMOUS SYSTEMS 236 7.2 THE MONODROMY MATRIX 240 7.3 THE
POINCARE MAP 242 7.4 MECHANISMS OF LOSING STABILITY 248 7.4.1 BRANCH
POINTS OF PERIODIC SOLUTIONS 250 7.4.2 PERIOD DOUBLING 255 7.4.3
BIFURCATION INTO TORUS 263 7.5 CALCULATING THE MONODROMY MATRIX 267
7.5.1 A POSTERIORI CALCULATION 267 7.5.2 MONODROMY MATRIX AS BY-PRODUCT
OF SHOOTING 269 7.5.3 NUMERICAL ASPECTS 270 7.6 CALCULATING BRANCHING
BEHAVIOR 272 7.7 FURTHER EXAMPLES AND PHENOMENA 280 8 QUALITATIVE
INSTRUMENTS 283 8.1 SIGNIFICANCE 283 8.2 SINGULARITY THEORY FOR ONE
SCALAR EQUATION 284 8.3 THE ELEMENTARY CATASTROPHES 293 8.3.1 THE FOLD
(REQUIRES ONE PARAMETER, Y) 293 8.3.2 THE CUSP (REQUIRES TWO PARAMETERS,
5, ) 294 8.3.3 THE SWALLOWTAIL (REQUIRES THREE PARAMETERS, Y, 8, ) 295
8.4 ZEROTH-ORDER REACTION IN A CSTR 297 8.5 CENTER MANIFOLDS 300 9 CHAOS
305 9.1 FLOWS AND ATTRACTORS 305 9.2 EXAMPLES OF STRANGE ATTRACTORS 311
9.3 ROUTES TO CHAOS 316 9.3.1 ROUTE VIA TORUS BIFURCATION 316 9.3.2
PERIOD DOUBLING ROUTE 317 9.3.3 INTERMITTENCY 317 9.4 CHARACTERIZATION
OF STRANGE ATTRACTORS 318 9.4.1 FRACTAL DIMENSION 318 9.4.2 LIAPUNOV
EXPONENTS 321 9.4.3 POWER SPECTRA 326 APPENDIXES 329 APPENDIX 1. SOME
ELEMENTARY FACTS FROM ODES 329 APPENDIX 2. IMPLICIT FUNCTION THEOREM 331
APPENDIX 3. SOME BASIC FACTS FROM LINEAR ALGEBRA 332 APPENDIX 4.
RUNGE-KUTTA-FEHLBERG METHODS 333 APPENDIX 5. TRANSFORMATION INTO
STANDARD FORM 334 APPENDIX 6. NUMERICAL SOFTWARE AND PACKAGES 336
APPENDIX 7 BASIC GROUPS 337 REFERENCES 339 INDEX 359
|
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| dewey-ones | 515 - Analysis |
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| isbn | 0444012508 |
| language | English |
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| spelling | Seydel, Rüdiger 1947- Verfasser (DE-588)13662782X aut From equilibrium to chaos practical bifurcation and stability analysis Rüdiger Seydel New York u.a. Elsevier 1988 XV, 367 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 339 - 358. - 2. Aufl. u.d.T.: Practical bifurcation and stability analysis Bifurcation, Théorie de la Stabilité Équations différentielles non linéaires Bifurcation theory Differential equations, Nonlinear Stability Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Chaotisches System (DE-588)4316104-2 s Stabilität (DE-588)4056693-6 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001454316&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seydel, Rüdiger 1947- From equilibrium to chaos practical bifurcation and stability analysis Bifurcation, Théorie de la Stabilité Équations différentielles non linéaires Bifurcation theory Differential equations, Nonlinear Stability Verzweigung Mathematik (DE-588)4078889-1 gnd Stabilität (DE-588)4056693-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4056693-6 (DE-588)4316104-2 |
| title | From equilibrium to chaos practical bifurcation and stability analysis |
| title_auth | From equilibrium to chaos practical bifurcation and stability analysis |
| title_exact_search | From equilibrium to chaos practical bifurcation and stability analysis |
| title_full | From equilibrium to chaos practical bifurcation and stability analysis Rüdiger Seydel |
| title_fullStr | From equilibrium to chaos practical bifurcation and stability analysis Rüdiger Seydel |
| title_full_unstemmed | From equilibrium to chaos practical bifurcation and stability analysis Rüdiger Seydel |
| title_short | From equilibrium to chaos |
| title_sort | from equilibrium to chaos practical bifurcation and stability analysis |
| title_sub | practical bifurcation and stability analysis |
| topic | Bifurcation, Théorie de la Stabilité Équations différentielles non linéaires Bifurcation theory Differential equations, Nonlinear Stability Verzweigung Mathematik (DE-588)4078889-1 gnd Stabilität (DE-588)4056693-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Bifurcation, Théorie de la Stabilité Équations différentielles non linéaires Bifurcation theory Differential equations, Nonlinear Stability Verzweigung Mathematik Stabilität Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001454316&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT seydelrudiger fromequilibriumtochaospracticalbifurcationandstabilityanalysis |