Catastrophe theory and bifurcation: applications to urban and regional systems
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
London
Croom Helm
1981
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| Series: | Croom Helm series in geography and environment.
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 331 S. zahlr. graph. Darst., Kt. |
| ISBN: | 0709927029 0520043707 |
Staff View
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| 245 | 1 | 0 | |a Catastrophe theory and bifurcation |b applications to urban and regional systems |c A. G. Wilson |
| 264 | 1 | |a London |b Croom Helm |c 1981 | |
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| 490 | 0 | |a Croom Helm series in geography and environment. | |
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| 650 | 4 | |a Geografie | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Catastrophes (Mathematics) | |
| 650 | 4 | |a Geography |x Mathematics | |
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Record in the Search Index
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| adam_text | CONTENTS Page PREFACE ACKNOWLEDGEMENTS CONTENTS LIST OF FIGURES LIST OF TABLES CHAPTER I. 1.1 A LAY GUIDE TO THE MATHEMATICS OF CATASTROPHE THEORY The nature of catastrophe theory 1 1 1.2 A preliminary outline of some examples 6 1.2.1 1.2.2 1.2.3 6 7 1.2.4 1.2.Б 1.3 A remark on scale The Zeeman catastrophe machine The micro scale: modal choice and the cusp catastrophe The meso scale: spatial structure and the fold catastrophe The macro scale: city growth and the cusp catastrophe An informal review of the mathematical concepts 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 CHAPTER 2. 8 10 12 14 An outline of the basic concepts 14 The mathematics of the elementarycatastrophe 18 Sets on the behaviour manifolds,anddelay conventions 20 The fold catastrophe 22 The cusp catastrophe 25 The remaining elementary and higher order catastrophes 28 DIFFERENTIAL EQUATIONS AND BIFURCATION 33 2.1 Differential equations and non-gradient systems 33 2.2 Dynamical systems and solutions to differential equations: a sketch of basic concepts 34 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 A preliminary note on types of graphical presentation Equilibrium points and trajectory sketching Static models embedded in dynamic frameworks Basic types of trajectory Bifurcation 34 37 38 39 42
2.3 Examples 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 CHAPTER 3. 3.1 Page 43 Introduction Growth equations Competition 1: the Lotka-Voi terraequations Competition 2: fixed resources Logistic growth equations for interacting populations Further extensions: linked subsystems and fluctuations APPLICATIONS OF DYNAMICAL SYSTEMS THEORY: A SURVEY OF APPROACHES 43 43 46 49 54 55 57 Introduction 57 3.2 Differential equations and catastrophe theory 58 3.3 Relative speeds of change: variables, parameters and constants; system description 59 3.4 Levels of approach 3.5 Qualitative vs. quantitative; deductive 3.6 60 inductive vs. 63. A new focus for planning applications of models NOTE ; CHAPTER 4. MACRO-SCALE APPLICATIONS 4.1 Introduction 4.2 Amson (1974): 4.3 Casti and Swain (1975) 1: 64 65 67 67 catastrophic modes of urban growth 69 central place theory 74 75 4.4 Casti and Swain (1975) 2: property prices 4.5 Poston and Wilson (1976): centre size another approach to 4.6 Mees (1975): Europe 4.7 Isard (1977): strategic elements of a theory of major structural change 4.8 Wagstaff (1978): 4.9 Dendrinos (1977): 78 the revival of cities in medieval 82 settlement pattern evolution slums in urban settings 4.10 Papageorgiou (1980): 4.11 Concluding comments sudden urban growth 82 84 88 89 92
Page CHAPTER 5. 5.1 5.2 5.3 5.4 BIFURCATION AT THE MESO-SCALE I: COMPARATIVE STATICS OF URBAN SPATIAL STRUCTURE Introduction The examples to be used The urban retail structure model 5.2.1 Other models with a similar structure 5.2.2 Residential structure 5.2.3 Interacting fields: the Lowry model 5.2.4 Disaggregation 5.2.5 Composite attractiveness factors 5.2.6 Theoretical foundations of the models: 5.2.7 mathematical programing Summary of the position reached 5.2.8 Equations for dynamical analysis Introduction 5.3.1 Retail model differential equations 5.3.2 Difference equations 5.3.3 Residential location 5.3.4 The Lowry model 5.3.5 Disaggregated models 5.3.6 Equilibrium point analysis 5.4.1 Introduction Retail model equilibrium point theory 5.4.2 Summary of results on retailing: towards a 5.4.3 theory of structural evolution 5.4.4 Residential location 5.4.5 The Lowry model Disaggregated models 5.4.6 5.4.7 Ecological analysis NOTES CHAPTER 6. 6.1 6.2 6.3 BIFURCATION AT THE MESO-SCALE II: THE DYNAMICS OF URBAN SPATIAL STRUCTURE Introduction 93 93 94 94 98 98 99 101 105 108 108 110 110 no 114 115 116 116 116 116 118 141 144 148 149 150 153 155 155 Disequilibrium, fluctuations and bifurcation 6.2.1 Introduction 6.2.2 Order from fluctuations: the Brussels school 6.2.3 The use of kinetic equations 6.2.4 Concluding comments 155 155 Control theoretic formulations 6.3.1 Introduction 6.3.2 A control problem in shopping centre location 6.3.3 Other possible applications 171 171 156 168 170 172 173
Page 6.4 Integrated approaches: central place theory 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.4.6 6.5 towards a new intra-urban Introduction: the bases of central place theory An alternative model representation for central place theory An example of an SIA model to be used as the basis for intra-urban central place theory Urban dynamics and the SIA model of central place theory The evolution of urban structure Comparisons with traditional central place theory 173 173 178 179 186 191 196 Some possibilities for further research 196 6.5.1 6.5.2 196 6.5.3 6.5.4 Introduction: development or evolution? Further research on models in the development mode An example of the evolution of new structures Concluding corments 199 201 MICRO-SCALE APPLICATIONS 203 NOTES 197 202 CHAPTER 7. 7.1 Introduction 203 7.2 Some general considerations 203 7.3 Hysteresis and modal choice 206 7.3.1 7.3.2 7.3.3 7.4 210 7.4.1 7.4.2 210 Some principles Model 1: attractiveness proportional to speed Model 2: addition of psychological factors 212 215 The speed-flow relationship and the fold catastrophe 218 7.5.1 7.5.2 7.6 206 208 210 Dynamic modal choice models and bifurcation 7.4.3 7.5 Hysteresis, catastrophe theory and modal choice A mechanism for hysteresis Empirical evidence The empirical results 218 A behavioural model and the fold catastrophe 219 Concluding comments 222
Page CHAPTER 8. 8.1 8.2 8.3 8.4 8.5 APPLICATIONS IN OTHER DISCIPLINES AND SOME NEW RESULTS FOR URBAN SYSTEMS Introduction Physical chemistry 8.2.1 Kinetic ______ equations: _______ interacting mixtures 8.2.2 Dissipative structures: order from fl uctuations 229 232 8.3.1 Introduction 232 8.3.2 Developmental biology 232 8.3.3 Evolutionary biology 234 Ecology 236 8.4.1 Population dynamics: differential equations 236 8.4.2 Population dynamics: difference equations 240 8.4.3 Travelling waves in ecological models 246 Economics շ48 Biology 8.5.1 8.5.2 8.5.3 8.6 225 225 226 226 Introduction Resource management Business cycles Applications to cities 8.6.1 Introduction and review 8.6.2 Urban models and Boolean algebra: analogues of genetic switching 8.6.3 Difference equations and shopping centres 248 249 253 256 256 256 260 CHAPTER 9. CONCLUDING COMMENTS APPENDIX 1 . MATHEMATICAL PROGRAMMING FORMULATIONS OF THE MAIN MODELS 271 267 Al .1 Introduction 271 Al.2 Entropy maximising and the shopping model 271 Al.З Consumers surplus 275 Al.4 Embedding: 278 Al.5 Accessibility maximising: Al.6 Random utility theory and group surplus Al.7 Application to residential location models Al .8 Mathematical programming versions of the Lowry model 285 APPENDIX 2. APPENDIX 3. APPENDIX 4. optimum centre size and location Leonardi s formulation 282 283 285 SOME ALTERNATIVE LAGRANGIAN FORMULATIONS 291 THE DERIVATIVES OF S. . 295 SHOPPING TRIP FLOW DERIVATIVES FOR THE DISAGGREGATED MODEL REFERENCES AND BIBLIOGRAPHY ÍNDEX 29? 301 315
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| id | DE-604.BV002298769 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:37Z |
| institution | BVB |
| isbn | 0709927029 0520043707 |
| language | English |
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| physical | 331 S. zahlr. graph. Darst., Kt. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Croom Helm |
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| series2 | Croom Helm series in geography and environment. |
| spelling | Wilson, Alan G. Sir 1939- Verfasser (DE-588)121868060 aut Catastrophe theory and bifurcation applications to urban and regional systems A. G. Wilson London Croom Helm 1981 331 S. zahlr. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Croom Helm series in geography and environment. Bifurcation, Théorie de la Catastrophes, Théorie des Géographie - Mathématiques Geografie Mathematik Bifurcation theory Catastrophes (Mathematics) Geography Mathematics Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilson, Alan G. Sir 1939- Catastrophe theory and bifurcation applications to urban and regional systems Bifurcation, Théorie de la Catastrophes, Théorie des Géographie - Mathématiques Geografie Mathematik Bifurcation theory Catastrophes (Mathematics) Geography Mathematics |
| title | Catastrophe theory and bifurcation applications to urban and regional systems |
| title_auth | Catastrophe theory and bifurcation applications to urban and regional systems |
| title_exact_search | Catastrophe theory and bifurcation applications to urban and regional systems |
| title_full | Catastrophe theory and bifurcation applications to urban and regional systems A. G. Wilson |
| title_fullStr | Catastrophe theory and bifurcation applications to urban and regional systems A. G. Wilson |
| title_full_unstemmed | Catastrophe theory and bifurcation applications to urban and regional systems A. G. Wilson |
| title_short | Catastrophe theory and bifurcation |
| title_sort | catastrophe theory and bifurcation applications to urban and regional systems |
| title_sub | applications to urban and regional systems |
| topic | Bifurcation, Théorie de la Catastrophes, Théorie des Géographie - Mathématiques Geografie Mathematik Bifurcation theory Catastrophes (Mathematics) Geography Mathematics |
| topic_facet | Bifurcation, Théorie de la Catastrophes, Théorie des Géographie - Mathématiques Geografie Mathematik Bifurcation theory Catastrophes (Mathematics) Geography Mathematics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wilsonalang catastrophetheoryandbifurcationapplicationstourbanandregionalsystems |