Multiple parameter stability theory and its applications: bifurcations, catastrophes, instabilities, ...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon
1986
|
| Series: | The Oxford engineering science series.
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 283 S. |
| ISBN: | 0198561709 |
Staff View
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| 245 | 1 | 0 | |a Multiple parameter stability theory and its applications |b bifurcations, catastrophes, instabilities, ... |
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Record in the Search Index
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| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 Introductory remarks 1
1.2 Modelling of reality 4
1.3 Mathematical formulation and basic definitions 7
1.4 Stability in autonomous systems 12
1.5 Autonomous systems with parameters 23
1.6 Classification of autonomous systems 26
2 POTENTIAL SYSTEMS 35
2.1 Potential function and stability of equilibrium states 35
2.2 Classification of critical conditions 41
2.3 Equilibrium surface via the multiple parameter perturba¬
tion technique 43
2.3.1 Regular (non critical) equilibrium states 43
2.3.2 General critical points 44
2.4 Simple general points and elementary catastrophes 48
2.4.1 General points of order 2 48
2.4.2 General points of order 3 (singular general point) 52
2.4.3 General points of order 4 and higher order 56
2.5 Two fold general critical points 57
2.5.1 Equilibrium surface and connection with umbilics 57
2.5.2 Critical zone 60
2.6 Special critical points and imperfection sensitivity 62
2.7 Concluding remarks 77
3 STATIC INSTABILITY OF AUTONOMOUS
SYSTEMS 79
3.1 One parameter systems 79
3.1.1 Simple critical points (divergence) 83
3.1.2 Simple bifurcation points 92
3.1.3 Stability of equilibrium paths in the vicinity of simple
bifurcation points 100
3.1.4 Compound branching 106
3.1.5 Imperfection sensitivity of critical points 110
3.2 Multiple parameter systems 122
3.2.1 Classification of critical points 122
3.2.2 Simple general points of order 2 123
3.2.3 Simple general points of order 3 (singular general
points) 135
3.2.4 Compound general points 141
xii CONTENTS
3.2.5 Special critical points 144
3.3 Concluding remarks 154
4 DYNAMIC INSTABILITY OF AUTONOMOUS
SYSTEMS 156
4.1 Introductory remarks 156
4.2 Non linear oscillations and the method of harmonic
balancing 157
4.3 An intrinsic method of harmonic analysis 161
4.4 One parameter systems ¦ 167
4.4.1 Hopf bifurcation 167
4.4.2 An illustrative example 179
4.4.3 Flat Hopf bifurcation 182
4.4.4 Symmetric bifurcation (tri furcation) 183
4.5 Alternative formulation of one parameter systems 188
4.5.1 Double Hopf bifurcation 192
4.5.2 Cusp bifurcation 196
4.5.3 Tangential bifurcation 200
4.6 Stability of limit cycles 203
4.6.1 Hopf bifurcation 206
4.6.2 Symmetric bifurcation (tri furcation) 207
4.7 Multiple parameter systems 208
4.7.1 Generalized Hopf bifurcation No. 1 211
4.7.2 Generalized Hopf bifurcation No. 2 214
4.7.3 Generalized Hopf bifurcation No. 3 218
4.7.4 More generalized bifurcations 219
4.8 Concluding remarks 223
5 APPLICATIONS 225
5.1 Potential systems in mechanics 225
5.1.1 A structural model 225
5.1.2 Columns on elastic foundations 229
5.1.3 Experimental results 232
5.2 Autonomous mechanical and electrical systems 233
5.2.1 A mechanical system 234
5.2.2 Static instability of a non linear network 237
5.2.3 Hopf bifurcation associated with a non linear
network 239
5.2.4 A mechanical system and its electrical analogue 242
5.3 Thermodynamics: phase transitions 250
5.4 Bio chemical processes (static instability) 251
5.5 The Brusselator 253
5.6 Aircraft at high angles of attack 257
5.7 Urban systems 259
CONTENTS xiii
6 CONCLUDING REMARKS 262
APPENDIX 267
REFERENCES 270
INDEX 279
|
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| id | DE-604.BV002290505 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:28Z |
| institution | BVB |
| isbn | 0198561709 |
| language | English |
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| physical | XIII, 283 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Clarendon |
| record_format | marc |
| series | The Oxford engineering science series. |
| series2 | The Oxford engineering science series. |
| spelling | Huseyin, Koncay Verfasser aut Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... Oxford Clarendon 1986 XIII, 283 S. txt rdacontent n rdamedia nc rdacarrier The Oxford engineering science series. 18 Stabilité Systèmes, Analyse de Stability System analysis Systemanalyse (DE-588)4116673-5 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Systemanalyse (DE-588)4116673-5 s Stabilität (DE-588)4056693-6 s DE-604 The Oxford engineering science series. 18 (DE-604)BV001897240 18. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huseyin, Koncay Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... The Oxford engineering science series. Stabilité Systèmes, Analyse de Stability System analysis Systemanalyse (DE-588)4116673-5 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4116673-5 (DE-588)4056693-6 |
| title | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_auth | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_exact_search | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_full | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_fullStr | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_full_unstemmed | Multiple parameter stability theory and its applications bifurcations, catastrophes, instabilities, ... |
| title_short | Multiple parameter stability theory and its applications |
| title_sort | multiple parameter stability theory and its applications bifurcations catastrophes instabilities |
| title_sub | bifurcations, catastrophes, instabilities, ... |
| topic | Stabilité Systèmes, Analyse de Stability System analysis Systemanalyse (DE-588)4116673-5 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Stabilité Systèmes, Analyse de Stability System analysis Systemanalyse Stabilität |
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