Surveying a dynamical system: a study of the Gray Scott reaction in a two-phase reactor
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman
1995
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
341 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 328 S. graph. Darst. |
| ISBN: | 0582246881 |
Staff View
MARC
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| 100 | 1 | |a Alhumaizi, Khalid |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Surveying a dynamical system |b a study of the Gray Scott reaction in a two-phase reactor |c Khalid Alhumaizi and Rutherford Aris |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman |c 1995 | |
| 300 | |a 328 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 341 | |
| 650 | 4 | |a Bifurcation theory | |
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| 650 | 4 | |a Differentiable dynamical systems | |
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Record in the Search Index
| _version_ | 1804125135991472128 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1. The Gray Scott cubic autocatalator 3
1.2. Multiplicity of steady states 7
1.3. Stability of the steady state. Hopf bifurcation 10
1.4. Stability of periodic solutions. Chaos 15
1.5. How to use this book 15
2 MATHEMATICAL MODELLING 18
2.1 Cubic Autocatalysis in a CSTR 19
2.2 Model I: Two tank System Coupled Through the Reactant A 21
2.2.1 Special Cases 24
2.3 Model II: Two tank System Coupled Through the Autocatalyst B 27
2.3.1 Special Cases 30
2.4 Isothermal and Nonisothermal Systems 33
3 STEADY STATE ANALYSIS 35
3.1 Static Bifurcation 35
3.2 Singularity Theory 38
4 STEADY STATE ANALYSIS: MODEL I 49
4.1 Steady State Relationship 49
4.2 Singularity Theory 52
4.2.1 Codimension one Singularities 52
4.2.2 Codimension two Singularities 63
4.2.3 Codimension three Singularities 71
5 STEADY STATE ANALYSIS: MODEL II 72
5.1 Steady State Relationship 72
5.2 Singularity Theory 74
5.2.1 Codimension one Singularities 74
5.2.2 Codimension two Singularities 88
5.2.3 Codimension three Singularities 95
6 DYNAMICS ¦ THEORY 96
6.1 Hopf Bifurcation Theorem 96
6.2 Type one Degenerate Bifurcations 102
6.3 Type two and Type three Degeneracies 106
6.3.1 Hon, 108
6.3.2 Hko HO
6.3.3 Hn 113
6.4 Secondary Bifurcations 117
7 DYNAMICS MODEL 1 123
7.1 Hopf Bifurcation 123
7.2 Degeneracies Type 1 129
7.2.1 Fi: Double zero Eigenvalues 129
7.2.2 F2: Pure Imaginary Pair and a Simple Zero Eigenvalue 131
7.2.3 Gi: Triple zero Eigenvalues 135
7.3 Degeneracies Type II 135
7.3.1 Hoi 136
7.3.2 H02 149
7.4 Degeneracies Type III 153
7.4.1 Hio 154
7.4.2 H20 168
7.4.3 Hn 176
8 DYNAMICS MODEL II 183
8.1 Hopf Bifurcation 183
8.2 Codimension one Singularities 185
8.3 F2: Pure Imaginary Pair and Simple Zero Eigenvalue 204
8.4 Codimension two Singularities 217
8.4.1 H02: Multiple Hopf Points 217
8.4.2 H20: Multiple Periodic Solutions 224
8.4.3 Hn: Isolated Periodic Solutions 226
9 CHAOS THEORY 227
9.1 Deterministic Chaos 228
9.1.1 Lyapunov Exponents 229
9.1.2 Poincare Map and Return Map 232
9.1.3 Power Spectra 234
9.2 Routes to Chaos 236
9.2.1 Local Bifurcations 236
9.2.2 Global Bifurcations 238
10 CHAOS MODEL I 241
10.1 Period doubling in the Parameter Space 241
10.2 Chaotic Behaviour 244
10.2.1 Lyapunov Exponents 248
10.2.2 Phase Trajectories 250
10.2.3 Poincare Map 263
10.2.4 Power Spectra 271
11 CHAOS MODEL n 275
11.1 Period doubling in the Parameter Space 275
11.2 Chaotic Behaviour Case 1 280
11.2.1 Feigenbaum s Number 285
11.2.2 Lyapunov Exponents 286
11.2.3 Phase Trajectories and Power Spectra 288
11.2.4 Poincare Map 294
11.3 Chaotic Behaviour Case II 301
11.3.1 Feigenbaum s Number 301
11.3.2 Lyapunov Exponents 302
11.3.3 Phase Trajectories 302
11.3.4 Poincare Map 304
12 SUMMARY AND CONCLUSIONS 306
12.1 Steady state Analysis 307
12.2 Dynamic Analysis 308
12.3 Chaotic Behaviour 309
12.4 Conclusions 310
BIBLIOGRAPHY 312
INDEX 322
|
| any_adam_object | 1 |
| author | Alhumaizi, Khalid Aris, Rutherford 1929-2005 |
| author_GND | (DE-588)12346420X |
| author_facet | Alhumaizi, Khalid Aris, Rutherford 1929-2005 |
| author_role | aut aut |
| author_sort | Alhumaizi, Khalid |
| author_variant | k a ka r a ra |
| building | Verbundindex |
| bvnumber | BV010657027 |
| ctrlnum | (OCoLC)246851858 (DE-599)BVBBV010657027 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010657027 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:45Z |
| institution | BVB |
| isbn | 0582246881 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007113477 |
| oclc_num | 246851858 |
| open_access_boolean | |
| owner | DE-12 DE-188 |
| owner_facet | DE-12 DE-188 |
| physical | 328 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Alhumaizi, Khalid Verfasser aut Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor Khalid Alhumaizi and Rutherford Aris 1. publ. Harlow, Essex Longman 1995 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 341 Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Zweiphasensystem (DE-588)4216838-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Mathematisches Modell (DE-588)4114528-8 s Zweiphasensystem (DE-588)4216838-7 s DE-604 Aris, Rutherford 1929-2005 Verfasser (DE-588)12346420X aut Pitman research notes in mathematics series 341 (DE-604)BV000022845 341 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007113477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alhumaizi, Khalid Aris, Rutherford 1929-2005 Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor Pitman research notes in mathematics series Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Zweiphasensystem (DE-588)4216838-7 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4114528-8 (DE-588)4216838-7 |
| title | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor |
| title_auth | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor |
| title_exact_search | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor |
| title_full | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor Khalid Alhumaizi and Rutherford Aris |
| title_fullStr | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor Khalid Alhumaizi and Rutherford Aris |
| title_full_unstemmed | Surveying a dynamical system a study of the Gray Scott reaction in a two-phase reactor Khalid Alhumaizi and Rutherford Aris |
| title_short | Surveying a dynamical system |
| title_sort | surveying a dynamical system a study of the gray scott reaction in a two phase reactor |
| title_sub | a study of the Gray Scott reaction in a two-phase reactor |
| topic | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Zweiphasensystem (DE-588)4216838-7 gnd |
| topic_facet | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Dynamisches System Mathematisches Modell Zweiphasensystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007113477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
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