Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1996
|
| Schriftenreihe: | [World scientific series on nonlinear science
21 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007572085&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 326 S. graph. Darst. |
| ISBN: | 9810226284 |
Internformat
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| 245 | 1 | 0 | |a Hopf bifurcation analysis |b a frequency domain approach |c Jorge L. Moiola ; Guanrong Chen |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1996 | |
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| 650 | 7 | |a Equações diferenciais ordinárias (análise) |2 larpcal | |
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| 650 | 7 | |a Teoria qualitativa |2 larpcal | |
| 650 | 7 | |a Équations différentielles non linéaires - Analyse numérique |2 ram | |
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| 650 | 4 | |a Differential equations, Nonlinear |x Numerical solutions | |
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Datensatz im Suchindex
| _version_ | 1819255165447831552 |
|---|---|
| adam_text | M. I WORLD SCIENTIFIC SERIES ON (-% E!*» A 11.1 44 NONLINEAR SCIENCE ^
SERIESA VO121 ISERIES EDITOR: LEON O. CHUA HOPF BIFURCATION HHHLVSIS H
FREQUENCY DOMAIN APPROACH I JORGE L MOIOLA UNIVERSLDAD NACIONAL DEL SUR,
ARGENTINA GUANRONG CHEN UNIVERSITY OF HOUSTON, TEXAS, USA WORLD
SCIENTIFIC SINGAPORE * NEW JERSEY LONDON »HONGKONG CONTENTS 1.
INTRODUCTION 1 1.1 STABILITY BIFURCATIONS 3 1.2 CENTER MANIFOLD THEOREM
8 1.3 LIMIT CYCLES AND DEGENERATE HOPF BIFURCATIONS 11 2. THE HOPF
BIFURCATION THEOREM 13 2.1 INTRODUCTION 14 2.2 THE HOPF BIFURCATION
THEOREM IN THE TIME DOMAIN 15 2.2.1 PRELIMINARIES 16 2.2.2 THE HOPF
BIFURCATION THEOREM 20 2.3 THE HOPF THEOREM IN THE FREQUENCY DOMAIN 21
2.4 EQUIVALENCE OF THE TWO HOPF THEOREMS 26 2.5 ADVANTAGES OF THE
FREQUENCY DOMAIN APPROACH 31 2.6 AN APPLICATION OF THE GRAPHICAL HOPF
THEOREM 34 3. CONTINUATION OF BIFURCATION CURVES ON THE PARAMETER PLANE
43 3.1 INTRODUCTION 44 3.2 STATIC AND- DYNAMIC BIFURCATIONS .45 3.2.1
FORMULATION OF ELEMENTARY BIFURCATION CONDITIONS 45 3.2.2 APPLICATIONS
OF THE FREQUENCY DOMAIN FORMULAS 51 3.2.2.1 THE SADDLE-NODE BIFURCATION
51 3.2.2.2 THE TRANSCRITICAL BIFURCATION .-, 52 3.2.2.3 THE HYSTERESIS
BIFURCATION 54 3.2.2.4 THE PITCHFORK BIFURCATION .56 3.2.2.5 STATIC
BIFURCATION IN CHEMICAL REACTOR MODELS 58 3.3 BIFURCATION ANALYSIS IN
THE FREQUENCY DOMAIN 62 3.3.1 FORMULATION OF MULTIPLE CROSSINGS AND
DETERMINATION OF DEGENERACIES * 62 3.3.2 APPLICATIONS OF THE FREQUENCY
DOMAIN FORMULAS TO MULTIPLE BIFURCATIONS 67 3.4 DEGENERATE HOPF
BIFURCATIONS OF CO-DIMENSION 1 76 XLLL XIV CONTENTS 3.5 APPLICATIONS AND
EXAMPLES 87 3.5.1 CONTINUATION OF BIFURCATION CURVES IN THE REACTOR WITH
CONSECUTIVE REACTIONS 87 3.5.2 CONTINUATION OF BIFURCATION CURVES IN THE
REACTOR WITH EXTRANEOUS THERMAL CAPACITANCE 96 4. DEGENERATE
BIFURCATIONS IN THE SPACE OF SYSTEM PARAMETERS 99 4.1 INTRODUCTION 100
4.2 MULTIPLICITY OF EQUILIBRIUM SOLUTIONS 102 4.3 MULTIPLE HOPF
BIFURCATION POINTS 105 4.4 DEGENERATE HOPF BIFURCATIONS AND THE
SINGULARITY THEORY 129 4.5 DEGENERATE HOPF BIFURCATIONS AND FEEDBACK
SYSTEMS 140 4.6 DEGENERATE HOPF BIFURCATIONS AND THE GRAPHICAL HOPF
THEOREM 150 4.6.1 DEGENERATE HOPF BIFURCATIONS OF THE HO M TYPE 151
4.6.2 DEGENERATE HOPF BIFURCATIONS OF THE HNO TYPE 156 4.7 SOME
APPLICATIONS 163 5. HIGH-ORDER HOPF BIFURCATION FORMULAS 171 5.1
INTRODUCTION 172 5.2 APPROXIMATION OF PERIODIC SOLUTIONS BY HIGHER-ORDER
FORMULAS 173 5.2.1 THE ALGORITHM 177 5.2.2 SOME APPLICATIONS 178 5.3
CONTINUATION OF PERIODIC SOLUTIONS: DEGENERATE CASES 191 5.4 LOCAL
BIFURCATION DIAGRAMS AND THE GRAPHICAL HOPF THEOREM 207 5.5 ALGORITHMS
FOR RECOVERING PERIODIC SOLUTIONS 209 5.5.1 THE ORIGINAL FORMULATION
(OF) 209 5.5.2 THE MODIFIED SCHEME (MS) 211 5.5.3 AN ITERATIVE ALGORITHM
(IA) 211 5.6 MULTIPLE LIMIT CYCLES AND NUMERICAL PROBLEMS 212 6. HOPF
BIFURCATION IN NONLINEAR SYSTEMS WITH TIME DELAYS : 219 6.1 INTRODUCTION
.220 6.2 CONDITIONS FOR DEGENERATE BIFURCATIONS IN TIME-DELAYED
SYSTEMS... 222 6.3 APPLICATIONS IN CONTROL SYSTEMS 228 6.3.1 VARIABLE
STRUCTURE CONTROL AND SMITH S PREDICTOR 228 6.3.2 CASCADE OF
TIME-DELAYED FEEDBACK INTEGRATORS 231 6.4 TIME-DELAYED FEEDBACK SYSTEMS:
THE GENERAL CASE 240 6.5 APPLICATION EXAMPLES 244 6.5.1 HOPF BIFURCATION
IN A PHASE-LOCKED LOOP CIRCUIT WITH TIME-DELAY 244 6.5.2 HOPF
BIFURCATION AND DEGENERACIES IN A NONLINEAR FEEDBACK CONTROL SYSTEM WITH
TWO TIME-DELAYS 247 CONTENTS XV 7. BIRTH OF MULTIPLE LIMIT CYCLES 255
7.1 INTRODUCTION 256 7.2 HARMONIC BALANCE AND CURVATURE COEFFICIENTS 258
7.3 SOME APPLICATION EXAMPLES 265 7.4 CONTROLLING THE MULTIPLICITIES OF
LIMIT CYCLES 273 APPENDIX 275 A. HIGHER-ORDER HOPF BIFURCATION FORMULAS:
PART I 275 B. HIGHER-ORDER HOPF BIFURCATION FORMULAS: PART II 294 C.
HIGHER-ORDER HOPF BIFURCATION FORMULAS: PART III 296 REFERENCES 299
AUTHOR INDEX 311 SUBJECT INDEX 319
|
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| author | Moiola, Jorge L. Chen, Guanrong 1948- |
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| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011276073 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:09:31Z |
| institution | BVB |
| isbn | 9810226284 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007572085 |
| oclc_num | 35224624 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-11 DE-188 |
| owner_facet | DE-384 DE-703 DE-11 DE-188 |
| physical | XV, 326 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| series2 | [World scientific series on nonlinear science / A] |
| spellingShingle | Moiola, Jorge L. Chen, Guanrong 1948- Hopf bifurcation analysis a frequency domain approach Bifurcation, Théorie de la ram Equações diferenciais (análise) larpcal Equações diferenciais ordinárias (análise) larpcal Teoria da bifurcação larpcal Teoria de sistemas e controle larpcal Teoria qualitativa larpcal Équations différentielles non linéaires - Analyse numérique ram Bifurcation theory Differential equations, Nonlinear Numerical solutions Hopf-Verzweigung (DE-588)4160648-6 gnd Frequenzbereichsdarstellung (DE-588)4199376-7 gnd |
| subject_GND | (DE-588)4160648-6 (DE-588)4199376-7 |
| title | Hopf bifurcation analysis a frequency domain approach |
| title_auth | Hopf bifurcation analysis a frequency domain approach |
| title_exact_search | Hopf bifurcation analysis a frequency domain approach |
| title_full | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola ; Guanrong Chen |
| title_fullStr | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola ; Guanrong Chen |
| title_full_unstemmed | Hopf bifurcation analysis a frequency domain approach Jorge L. Moiola ; Guanrong Chen |
| title_short | Hopf bifurcation analysis |
| title_sort | hopf bifurcation analysis a frequency domain approach |
| title_sub | a frequency domain approach |
| topic | Bifurcation, Théorie de la ram Equações diferenciais (análise) larpcal Equações diferenciais ordinárias (análise) larpcal Teoria da bifurcação larpcal Teoria de sistemas e controle larpcal Teoria qualitativa larpcal Équations différentielles non linéaires - Analyse numérique ram Bifurcation theory Differential equations, Nonlinear Numerical solutions Hopf-Verzweigung (DE-588)4160648-6 gnd Frequenzbereichsdarstellung (DE-588)4199376-7 gnd |
| topic_facet | Bifurcation, Théorie de la Equações diferenciais (análise) Equações diferenciais ordinárias (análise) Teoria da bifurcação Teoria de sistemas e controle Teoria qualitativa Équations différentielles non linéaires - Analyse numérique Bifurcation theory Differential equations, Nonlinear Numerical solutions Hopf-Verzweigung Frequenzbereichsdarstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007572085&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT moiolajorgel hopfbifurcationanalysisafrequencydomainapproach AT chenguanrong hopfbifurcationanalysisafrequencydomainapproach |