Nonlinear dynamical economics and chaotic motion:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1993
|
| Edition: | 2., rev. and enl. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 319 S. graph. Darst. |
| ISBN: | 3540568816 0387568816 |
Staff View
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| 245 | 1 | 0 | |a Nonlinear dynamical economics and chaotic motion |c Hans-Walter Lorenz |
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Record in the Search Index
| _version_ | 1804122473230237696 |
|---|---|
| adam_text | Contents
Introduction 1
1. Economic Dynamics, Linearities, and the Classical Mechanistic
Worldview 5
1.1. Some Reflections on the Origin of Economic Dynamics 6
1.2. The Deterministic Worldview and Deterministic Theories 13
1.3. The Dominance of Linear Dynamical Systems in Economics 19
2. Nonlinearities and Economic Dynamics 26
2.1. Preliminary Concepts 27
2.2. The Poincare Bendixson Theorem 39
2.2.1. The Existence of Limit Cycles 40
2.2.2. The Kaldor Model as a Prototype Model in Nonlinear
Economic Dynamics 43
2.2.3. A Classical Cross Dual Adjustment Process 47
2.3. The Uniqueness of Limit Cycles 51
2.3.1. The Lienard Equation and Related Tools 51
2.3.2. The Symmetric Case: Unique Cycles in a Modified Phillips
Model 54
2.3.3. The Asymmetric Case: Unique Cycles in a Kaldor Model 57
2.4. Predator Prey Models 61
2.4.1. The Dynamics of Conservative Dynamical Systems 61
2.4.2. Goodwin s Predator Prey Model of the Class Struggle 67
XIV Contents
2.4.3. Other Examples and Predator Prey Structures in
Dissipative Systems 69
2.5. Relaxation Oscillations 73
2.6. Irreversibility and Determinism in Dynamical Systems 77
3. Bifurcation Theory and Economic Dynamics 80
3.1. Preliminaries and Different Concepts of Structural Stability 81
3.2. Local Bifurcations in Continuous Time Dynamical Systems 87
3.2.1. Fold, Transcritical, and Pitchfork Bifurcations 87
3.2.2. The Hopf Bifurcation in Continuous Time Dynamical Systems .. .95
3.2.2.1. The Hopf Bifurcation in Business Cycle Theory 101
3.2.2.2. Closed Orbits in Optimal Economic Growth 107
3.3. Local Bifurcations in Discrete Time Dynamical Systems 110
3.3.1. Fold, Transcritical, Pitchfork, and Flip Bifurcations HO
3.3.2. The Hopf Bifurcation in Discrete Time Dynamical Systems 115
4. Chaotic Dynamics in Discrete Time Economic Models 119
4.1. Chaos in One Dimensional, Discrete Time Dynamical Systems 121
4.1.1. Basic Concepts 122
4.1.2. Chaos in Descriptive Growth Theory 138
4.1.3. Chaos in Discrete Time Models of Optimal Economic Growth .. 143
4.1.4. Other Economic Examples 146
4.2. Chaos in Higher Dimensional Discrete Time Systems 149
4.2.1. Some Basic Ideas 149
4.2.2. An Economic Example 153
4.3. Complex Transients in Discrete Time Dynamical Systems 157
4.3.1. Complex Transient Behavior in One Dimensional Systems 158
4.3.2. Horseshoes, Homoclinic Orbits, and Complicated
Invariant Sets 161
5. Chaotic Dynamics in Continuous Time Economic Models 16
5.1. Basic Ideas 167
5.2. The Coupling of Oscillators 174
5.2.1. Toroidal Motion I74
5.2.2. International Trade as the Coupling of Oscillators I80
5.3. The Forced Oscillator I82
5.3.1. Forced Oscillator Systems and Chaotic Motion l8^
5.3.2. Goodwins s Nonlinear Accelerator as a Forced Oscillator l8^
Contents XV
5.3.3. Keynesian Demand Policy as the Source of Chaotic Motion 187
5.3.4. Conclusion 192
5.4. Homoclinic Orbits and Spiral Type Attractors 192
5.4.1. The Shil nikov Scenario 193
5.4.2. Spiral Type Chaos in a Business Cycle Model with Inventories .. 195
6. Numerical Tools 201
6.1. Spectral Analysis 202
6.2. Dimension, Entropy, and Lyapunov Exponents 205
6.2.1. Phase Space Embedding 205
6.2.2. Fractal Dimensions 208
6.2.3. Correlation Dimension 211
6.2.4. Lyapunov Exponents 213
6.2.5. Kolmogorov Entropy 218
6.2.6. Summary 220
6.3. Are Economic Time Series Chaotic? 222
6.4. Predictability in the Face of Chaotic Dynamics 228
7. Catastrophe Theory and Economic Dynamics 233
7.1. Basic Ideas 234
7.2. The Kaldor Model in the Light of Catastrophe Theory 239
7.3. A Catastrophe Theoretical Approach to Stagflation 241
8. Concluding Remarks 244
Appendix 248
A.l. Basic Properties of Linear Dynamical Systems 249
A.2. Center Manifolds and the Reduction of (Effective) Dimensions 264
A.3. A Brief Introduction to the Theory of Lags and Operators 270
A.4. Numerical Simulations and Chaotic Dynamics in Theoretical
Economics 276
References 283
Name Index 309
Subject Index 315
|
| any_adam_object | 1 |
| author | Lorenz, Hans-Walter 1951- |
| author_GND | (DE-588)170210960 |
| author_facet | Lorenz, Hans-Walter 1951- |
| author_role | aut |
| author_sort | Lorenz, Hans-Walter 1951- |
| author_variant | h w l hwl |
| building | Verbundindex |
| bvnumber | BV008100146 |
| callnumber-first | H - Social Science |
| callnumber-label | HB145 |
| callnumber-raw | HB145.L67 1993 |
| callnumber-search | HB145.L67 1993 |
| callnumber-sort | HB 3145 L67 41993 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | QC 300 QC 330 QH 300 |
| ctrlnum | (OCoLC)28374781 (DE-599)BVBBV008100146 |
| dewey-full | 300/.1/5 300/.1/520 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 300 - Social sciences |
| dewey-raw | 300/.1/5 300/.1/5 20 |
| dewey-search | 300/.1/5 300/.1/5 20 |
| dewey-sort | 3300 11 15 |
| dewey-tens | 300 - Social sciences |
| discipline | Soziologie Wirtschaftswissenschaften |
| edition | 2., rev. and enl. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:14:26Z |
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| publisher | Springer |
| record_format | marc |
| spelling | Lorenz, Hans-Walter 1951- Verfasser (DE-588)170210960 aut Nonlinear dynamical economics and chaotic motion Hans-Walter Lorenz 2., rev. and enl. ed. Berlin [u.a.] Springer 1993 XV, 319 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos gtt Conjunctuur gtt Niet-lineaire dynamica gtt Statics and dynamics (Social sciences) Economics, Mathematical Differential equations, Nonlinear Chaotic behavior in systems Dynamische Makroökonomie (DE-588)4200428-7 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Konjunkturzyklus (DE-588)4032134-4 gnd rswk-swf Ökonometrisches Modell (DE-588)4043212-9 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 s Nichtlineares dynamisches System (DE-588)4126142-2 s Chaotisches System (DE-588)4316104-2 s DE-604 Ökonometrisches Modell (DE-588)4043212-9 s Chaostheorie (DE-588)4009754-7 s Konjunkturzyklus (DE-588)4032134-4 s 1\p DE-604 Chaos (DE-588)4191419-3 s 2\p DE-604 Ökonometrie (DE-588)4132280-0 s 3\p DE-604 Dynamisches System (DE-588)4013396-5 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005336177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lorenz, Hans-Walter 1951- Nonlinear dynamical economics and chaotic motion Chaos gtt Conjunctuur gtt Niet-lineaire dynamica gtt Statics and dynamics (Social sciences) Economics, Mathematical Differential equations, Nonlinear Chaotic behavior in systems Dynamische Makroökonomie (DE-588)4200428-7 gnd Chaotisches System (DE-588)4316104-2 gnd Chaos (DE-588)4191419-3 gnd Dynamisches System (DE-588)4013396-5 gnd Ökonometrie (DE-588)4132280-0 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Konjunkturzyklus (DE-588)4032134-4 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd |
| subject_GND | (DE-588)4200428-7 (DE-588)4316104-2 (DE-588)4191419-3 (DE-588)4013396-5 (DE-588)4132280-0 (DE-588)4009754-7 (DE-588)4126142-2 (DE-588)4032134-4 (DE-588)4043212-9 |
| title | Nonlinear dynamical economics and chaotic motion |
| title_auth | Nonlinear dynamical economics and chaotic motion |
| title_exact_search | Nonlinear dynamical economics and chaotic motion |
| title_full | Nonlinear dynamical economics and chaotic motion Hans-Walter Lorenz |
| title_fullStr | Nonlinear dynamical economics and chaotic motion Hans-Walter Lorenz |
| title_full_unstemmed | Nonlinear dynamical economics and chaotic motion Hans-Walter Lorenz |
| title_short | Nonlinear dynamical economics and chaotic motion |
| title_sort | nonlinear dynamical economics and chaotic motion |
| topic | Chaos gtt Conjunctuur gtt Niet-lineaire dynamica gtt Statics and dynamics (Social sciences) Economics, Mathematical Differential equations, Nonlinear Chaotic behavior in systems Dynamische Makroökonomie (DE-588)4200428-7 gnd Chaotisches System (DE-588)4316104-2 gnd Chaos (DE-588)4191419-3 gnd Dynamisches System (DE-588)4013396-5 gnd Ökonometrie (DE-588)4132280-0 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Konjunkturzyklus (DE-588)4032134-4 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd |
| topic_facet | Chaos Conjunctuur Niet-lineaire dynamica Statics and dynamics (Social sciences) Economics, Mathematical Differential equations, Nonlinear Chaotic behavior in systems Dynamische Makroökonomie Chaotisches System Dynamisches System Ökonometrie Chaostheorie Nichtlineares dynamisches System Konjunkturzyklus Ökonometrisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005336177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lorenzhanswalter nonlineardynamicaleconomicsandchaoticmotion |