Elements of applied bifurcation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1995
|
| Series: | Applied mathematical sciences
112 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 515 S. graph. Darst. |
| ISBN: | 0387944184 |
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| 100 | 1 | |a Kuznecov, Jurij A. |d 1945- |e Verfasser |0 (DE-588)113390831 |4 aut | |
| 245 | 1 | 0 | |a Elements of applied bifurcation theory |c Yuri A. Kuznetsov |
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| 300 | |a XV, 515 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | YURI A. KUZNETSOV
ELEMENTS OF APPLIED
BIFURCATION THEORY
WITH 232 ILLUSTRATIONS
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO HONG KONG BARCELONA BUDAPEST
CONTENTS
PREFACE VII
1 INTRODUCTION TO DYNAMICAL SYSTEMS 1
1.1 DEFINITION OF DYNAMICAL SYSTEM 1
1.2 ORBITS AND PHASE PORTRAITS 8
1.3 INVARIANT SETS 10
1.4 DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 17
1.5 POINCAREMAPS 22
1.6 EXERCISES 29
1.7 APPENDIX 1: INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS DEFINED BY
REACTION-DIFFUSION EQUATIONS 30
1.8 APPENDIX 2: BIBLIOGRAPHICAL NOTES 34
2 TOPOIOGICAL EQUIVALENCE, BIFURCATIONS, AND STRUCTURAL STABILITY OF
DYNAMICAL SYSTEMS 36
2.1 EQUIVALENCE OF DYNAMICAL SYSTEMS 36
2.2 TOPOIOGICAL CLASSIFICATION OF GENERIC EQUILIBRIA AND FIXED POINTS .
42
2.3 BIFURCATIONS AND BIFURCATION DIAGRAMS 53
2.4 TOPOIOGICAL NORMAL FORMS FOR BIFURCATIONS 59
2.5 STRUCTURAL STABILITY 63
2.6 EXERCISES 67
2.7 APPENDIX: BIBLIOGRAPHICAL NOTES 71
3 ONE-PARAMETER BIFURCATIONS OF EQUILIBRIA IN CONTINUOUS-TIME
SYSTEMS 73
3.1 SIMPLEST BIFURCATION CONDITIONS 73
3.2 THE NORMAL FORM OF THE FOLD BIFURCATION 74
3.3 FOLD BIFURCATION THEOREM 77
3.4 THE NORMAL FORM OF THE HOPF BIFURCATION 79
3.5 HOPF BIFURCATION THEOREM 84
3.6 EXERCISES 97
3.7 APPENDIX 1: PROOFOF LEMMA 3.2 99
3.8 APPENDIX 2: BIBLIOGRAPHICAL NOTES 101
XIV CONTENTS
4 ONE-PARAMETER BIFURCATIONS OF FIXED POINTS IN DISCRETE-TIME
SYSTEMS 103
4.1 SIMPLEST BIFURCATION CONDITIONS 103
4.2 THE NORMAL FORM OF THE FOLD BIFURCATION 104
4.3 FOLD BIFURCATION THEOREM 106
4.4 THE NORMAL FORM OF THE FLIP BIFURCATION 108
4.5 FLIP BIFURCATION THEOREM 111
4.6 THE NORMAL FORM OF THE NEIMARK-SACKER BIFURCATION 114
4.7 NEIMARK-SACKER BIFURCATION THEOREM 118
4.8 EXERCISES 126
4.9 APPENDIX 1: FEIGENBAUM S UNIVERSALITY 127
4.10 APPENDIX 2: PROOF OF LEMMA 4.3 131
4.11 APPENDIX 3
: BIBLIOGRAPHICAL NOTES 136
5 BIFURCATIONS OF EQUILIBRIA AND PERIODIC ORBITS IN N-DIMENSIONAL
SYSTEMS 138
5.1 CENTER MANIFOLD THEOREMS 138
5.2 CENTER MANIFOLDS IN PARAMETER-DEPENDENT SYSTEMS 144
5.3 BIFURCATIONS OF LIMIT CYCLES 148
5.4 COMPUTATION OF CENTER MANIFOLDS 151
5.5 EXERCISES 166
5.6 APPENDIX 1: HOPF BIFURCATION IN REACTION-DIFFUSION SYSTEMS ON
THE INTERVAL WITH DIRICHLET BOUNDARY CONDITIONS 168
5.7 APPENDIX 2: BIBLIOGRAPHICAL NOTES 176
6 BIFURCATIONS OF ORBITS HOMOCLINIC AND HETEROCLINIC TO HYPERBOLIC
EQUILIBRIA 178
6.1 HOMOCLINIC AND HETEROCLINIC ORBITS 178
6.2 ANDRONOV-LEONTOVICH THEOREM 183
6.3 HOMOCLINIC BIFURCATIONS IN THREE-DIMENSIONAL SYSTEMS:
SHIFNIKOV THEOREMS 193
6.4 HOMOCLINIC BIFURCATIONS IN N-DIMENSIONAL SYSTEMS 208
6.5 EXERCISES 210
6.6 APPENDIX 1: BIBLIOGRAPHICAL NOTES 212
7 OTHER ONE-PARAMETER BIFURCATIONS IN CONTINUOUS-TIME SYSTEMS 214
7.1 CODIM 1 BIFURCATIONS OF HOMOCLINIC ORBITS TO NONHYPERBOLIC
EQUILIBRIA 214
7.2 EXOTIC BIFURCATIONS 227
7.3 BIFURCATIONS ON INVARIANT TORI 229
7.4 BIFURCATIONS IN SYMMETRIE SYSTEMS 236
7.5 EXERCISES 248
7.6 APPENDIX 1: BIBLIOGRAPHICAL NOTES 250
CONTENTS XV
8 TWO-PARAMETER BIFURCATIONS OF EQUILIBRIA IN CONTINUOUS-TIME
DYNAMICAL SYSTEMS 252
8.1 LIST OF CODIM 2 BIFURCATIONS OF EQUILIBRIA 252
8.2 CUSP BIFURCATION 259
8.3 BAUTIN (GENERALIZED HOPF) BIFURCATION 265
8.4 BOGDANOV-TAKENS (DOUBLE-ZERO) BIFURCATION 272
8.5 FOLD-HOPF (ZERO-PAIR) BIFURCATION 287
8.6 HOPF-HOPF BIFURCATION 305
8.7 EXERCISES 324
8.8 APPENDIX 1: LIMIT CYCLES AND HOMOCLINIC ORBITS OF THE
BOGDANOV-TAKENS NORMAL FORM 336
8.9 APPENDIX 2: BIBLIOGRAPHICAL NOTES 345
9 TWO-PARAMETER BIFURCATIONS OF FIXED POINTS IN DISCRETE-TIME
DYNAMICAL SYSTEMS 347
9.1 LIST OF CODIM 2 BIFURCATIONS OF FIXED POINTS 347
9.2 CUSP BIFURCATION 351
9.3 GENERALIZED FLIP BIFURCATION 354
9.4 CHENCINER (GENERALIZED NEIMARK-SACKER) BIFURCATION 357
9.5 STRONG RESONANCES 362
9.6 CODIM 2 BIFURCATIONS OF LIMIT CYCLES 399
9.7 EXERCISES 408
9.8 APPENDIX 1: BIBLIOGRAPHICAL NOTES 412
10 NUMERICAL ANALYSIS OF BIFURCATIONS 414
10.1 NUMERICAL ANALYSIS AT FIXED PARAMETER VALUES 415
10.2 ONE-PARAMETER BIFURCATION ANALYSIS 429
10.3 TWO-PARAMETER BIFURCATION ANALYSIS 449
10.4 CONTINUATION STRATEGY 455
10.5 EXERCISES 456
10.6 APPENDIX 1: CONVERGENCE THEOREMS FOR NEWTON METHODS ...
. 464
10.7 APPENDIX 2: NUMERICAL ANALYSIS OF HOMOCLINIC BIFURCATIONS . . . 465
10.8 APPENDIX 3
: BIBLIOGRAPHICAL NOTES 472
A BASIC NOTIONS FROM ALGEBRA, ANALYSIS, AND GEOMETRY 477
A.
L ALGEBRA 477
A.2 ANALYSIS 482
A.3 GEOMETRY 485
REFERENCES 487
INDEX 503
|
| any_adam_object | 1 |
| author | Kuznecov, Jurij A. 1945- |
| author_GND | (DE-588)113390831 |
| author_facet | Kuznecov, Jurij A. 1945- |
| author_role | aut |
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| author_variant | j a k ja jak |
| building | Verbundindex |
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| dewey-full | 510 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515/.352 |
| dewey-search | 510 515/.352 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:50:27Z |
| institution | BVB |
| isbn | 0387944184 |
| language | English |
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| physical | XV, 515 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Kuznecov, Jurij A. 1945- Verfasser (DE-588)113390831 aut Elements of applied bifurcation theory Yuri A. Kuznetsov New York [u.a.] Springer 1995 XV, 515 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 112 Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Applied mathematical sciences 112 (DE-604)BV000005274 112 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006867075&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuznecov, Jurij A. 1945- Elements of applied bifurcation theory Applied mathematical sciences Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Elements of applied bifurcation theory |
| title_auth | Elements of applied bifurcation theory |
| title_exact_search | Elements of applied bifurcation theory |
| title_full | Elements of applied bifurcation theory Yuri A. Kuznetsov |
| title_fullStr | Elements of applied bifurcation theory Yuri A. Kuznetsov |
| title_full_unstemmed | Elements of applied bifurcation theory Yuri A. Kuznetsov |
| title_short | Elements of applied bifurcation theory |
| title_sort | elements of applied bifurcation theory |
| topic | Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006867075&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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