A philosophical analysis of chaos theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Palgrave MacMillan
[2017]
|
| Schriftenreihe: | New directions in the philosophy of science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 138 Seiten Illustrationen, Diagramme 22 cm |
| ISBN: | 9783319546629 9783319854489 |
Internformat
MARC
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| 100 | 1 | |a Zuchowski, Lena Christine |e Verfasser |0 (DE-588)1060471663 |4 aut | |
| 245 | 1 | 0 | |a A philosophical analysis of chaos theory |c Lena C. Zuchowski |
| 264 | 1 | |a Cham, Switzerland |b Palgrave MacMillan |c [2017] | |
| 300 | |a xiii, 138 Seiten |b Illustrationen, Diagramme |c 22 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a New directions in the philosophy of science | |
| 650 | 4 | |a Philosophy | |
| 650 | 4 | |a Philosophy and science | |
| 650 | 4 | |a Philosophy of Science | |
| 650 | 4 | |a Science, Humanities and Social Sciences, multidisciplinary | |
| 650 | 4 | |a Applications of Nonlinear Dynamics and Chaos Theory | |
| 650 | 4 | |a Naturwissenschaft | |
| 650 | 4 | |a Philosophie | |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Philosophie |0 (DE-588)4045791-6 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Chaotic behavior in systems | |
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| 653 | 0 | |a Chaotic behavior in systems | |
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Datensatz im Suchindex
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| adam_text |
Contents
1 Introduction i
2 Vertical and Horizontal Models in Chaos Theory 5
2.1 Introduction 5
2.2 Vertical and Horizontal Models 6
2.2.1 Vertical Models 7
2.2.2 Horizontal Models 14
2.3 A Lineage of Logistic Models 16
2.3.1 Continuous Logistic Model 16
2.3.2 Discrete Logistic Model 17
2.3.3 Iterated Logistic Model 20
2.4 A Lineage of Lorenz Models 27
2.4.1 Discrete Lorenz Model 27
2.4.2 Iterated Lorenz Model 31
2.5 Conclusion 34
3 Chaos Criteria and Definitions 37
3.1 Introduction 37
3.1.1 Sufficient Conditions and Criteria for Chaos 39
3.1.2 Outline of the Chapters Content 40
3.2 Diagnosis of Chaos in the Logistic Lineage 42
3.2.1 No Chaos in the Continuous Logistic Model 43
3.2.2 Stochastic Chaos in the Discrete Logistic Model 43
vii
viii CONTENTS
3.2.3 Devaney Chaos in the Iterated Logistic Model 46
3.3 Dynamical and Phenomenological Criteria for Chaos 48
3.3.1 Determinism: A Dynamical (Pre-)criterion 50
3.3.2 Transitivity 54
3.3.3 Periodicity 56
3.3.4 Aperiodicity 57
3.3.5 Sensitive Dependence on Initial Conditions 60
3.4 Analysis and Comparison of Chaos Definitions 66
3.4.1 Devaney Chaos 67
3.4.2 Mixing 69
3.4.3 Positive Lyapunov Exponents 71
3.4.4 Stochastic Chaos 72
3.4.5 Strange Attractors 74
3.5 Conclusion 77
4 Evaluation of Chaotic Models 81
4.1 Introduction 81
4.1.1 A Three-Step Framework for the Evaluation of
Vertical Chaotic Models 81
4.1.2 Outline of the Chapter’s Content 83
4.2 Evaluation of the Lineage of Logistic Models 86
4.2.1 Evaluation of the Discrete Logistic Model 87
4.2.2 Evaluation of the Iterated Logistic Model 93
4.3 Evaluation of Vertical Chaotic Models 98
4.3.1 Determining the Conditional to be Evaluated 98
4.3.2 Determining the Existence of Chaos 107
4.3.3 Determining Model Faithfulness 112
4.4 Evaluation of Horizontal Chaotic Models 116
4.4.1 Investigation of Mathematical Properties 116
4.4.2 Investigative Use 117
4.5 Smale’s 14th Problem 118
4.5.1 Chaotic Conditionals in the Lorenz Models 119
4.5.2 Construction of the Rigorous Lorenz Model 121
4.5.3 Behaviour of the Rigorous Lorenz Model 122
4.5.4 Evaluation of the Rigorous Lorenz Model 123
4.6 Conclusion 124
CONTENTS IX
5 Conclusion 127
5.1 Construction of Models in Chaos Theory 128
5.2 Diagnosis of Models as Being Chaotic 129
5.3 Evaluation of Chaotic Models 130
5.4 Interplay of Models as a Characteristic Feature
of Chaos Theory 131
Bibliography 133
Index 137 |
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| author | Zuchowski, Lena Christine |
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| illustrated | Illustrated |
| indexdate | 2024-08-25T00:01:46Z |
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| isbn | 9783319546629 9783319854489 |
| language | English |
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| physical | xiii, 138 Seiten Illustrationen, Diagramme 22 cm |
| publishDate | 2017 |
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| publisher | Palgrave MacMillan |
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| series2 | New directions in the philosophy of science |
| spelling | Zuchowski, Lena Christine Verfasser (DE-588)1060471663 aut A philosophical analysis of chaos theory Lena C. Zuchowski Cham, Switzerland Palgrave MacMillan [2017] xiii, 138 Seiten Illustrationen, Diagramme 22 cm txt rdacontent n rdamedia nc rdacarrier New directions in the philosophy of science Philosophy Philosophy and science Philosophy of Science Science, Humanities and Social Sciences, multidisciplinary Applications of Nonlinear Dynamics and Chaos Theory Naturwissenschaft Philosophie Chaostheorie (DE-588)4009754-7 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Chaotic behavior in systems Science / Philosophy Chaostheorie (DE-588)4009754-7 s Philosophie (DE-588)4045791-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-54663-6 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029927425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zuchowski, Lena Christine A philosophical analysis of chaos theory Philosophy Philosophy and science Philosophy of Science Science, Humanities and Social Sciences, multidisciplinary Applications of Nonlinear Dynamics and Chaos Theory Naturwissenschaft Philosophie Chaostheorie (DE-588)4009754-7 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4045791-6 |
| title | A philosophical analysis of chaos theory |
| title_auth | A philosophical analysis of chaos theory |
| title_exact_search | A philosophical analysis of chaos theory |
| title_full | A philosophical analysis of chaos theory Lena C. Zuchowski |
| title_fullStr | A philosophical analysis of chaos theory Lena C. Zuchowski |
| title_full_unstemmed | A philosophical analysis of chaos theory Lena C. Zuchowski |
| title_short | A philosophical analysis of chaos theory |
| title_sort | a philosophical analysis of chaos theory |
| topic | Philosophy Philosophy and science Philosophy of Science Science, Humanities and Social Sciences, multidisciplinary Applications of Nonlinear Dynamics and Chaos Theory Naturwissenschaft Philosophie Chaostheorie (DE-588)4009754-7 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Philosophy Philosophy and science Philosophy of Science Science, Humanities and Social Sciences, multidisciplinary Applications of Nonlinear Dynamics and Chaos Theory Naturwissenschaft Philosophie Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029927425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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