Discrete dynamical systems and chaos:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman Scientific & Technical
1992
New York Wiley |
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
62 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 282 S. graph. Darst. |
| ISBN: | 0582096375 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804122662830604288 |
|---|---|
| adam_text | Contents
CHAPTER 1. Discrete Dynamical Systems 1
SECTION 1. Generalities on Dynamical Systems 2
1. Dynamical processes 2
2. Stationary states 6
3. Stability of stationary states 7
4. Periodic orbits 10
5. Stability of periodic orbits 12
6. Limit points 13
SECTION 2. Examples of Discrete Dynamical Systems 18
1. One dimensional example:
blood cell biology 18
2. Two dimensional example:
population biology 19
3. Three dimensional example:
meteorology 22
4. Multi dimensional example:
neural networks 24
PROBLEMS 26
CHAPTER 2. One Dimensional Dynamical Systems 29
SECTION 1. Preliminaries on One Dimensional Systems.... 30
1. The cobweb method 30
2. Conjugacy 32
3. Linear and affine systems 36
SECTION 2. Nonlinear One Dimensional Systems 37
1. Stationary states and periodic orbits 37
2. Stability of stationary states and periodic orbits 38
SECTION 3. Global Behavior and Conjugacy 47
1. Global behavior 47
2. More on conjugacy 53
^ Contents
SECTION 4. Parameter Space Analysis 55
1. Bifurcation points and bifurcation diagrams 55
2. Period doubling bifurcation 57
3. Pitchfork bifurcation 60
4. Transcritical bifurcation 63
5. Fold bifurcation 64
PROBLEMS 69
CHAPTER 3. RQ, Functions and Matrices 73
SECTION 1. Structure of R1 74
1. Definition of R1 74
2. Linear combination and linear independence 79
3. Subspaces, basis and dimension 80
4. Functions and continuity 82
SECTION 2. Matrices 84
1. Definitions and operations 84
2. Determinant and rank 86
3. Invertible matrices and similarity 90
4. Eigenvalues and spectral radius 92
SECTION 3. Matrices as Linear Operators 95
1. The action of a matrix 95
2. Operator norm of a matrix 96
3. Kernel and image 98
4. Eigenvectors 100
5. Real canonical form 105
SECTION 5. Derivative and First Order Approximation 109
1. Derivative 109
2. First order approximation 110
PROBLEMS 112
CHAPTER 4. Discrete Linear Dynamical Systems 117
SECTION 1. Linear and Affine Processes 118
Discrete Dynamical Systems and Chaos
SECTION 2. Stability and Instability of the Origin 122
1. The origin as a sink 122
2. The origin as a source 125
SECTION 3. The Origin as a Saddle Point 127
1. The action of a real canonical form of M 128
2. The action of M 130
3. Comparing trajectories 136
4. Affine systems 137
SECTION 5. Eigenvalues with Modulus 1 141
1. The action of M on Xi 142
2. The action of M on X_i 143
3. The action of M on Xc 144
4. Conjugacy in the degenerate case 147
PROBLEMS 151
CHAPTER 5. Nonlinear Dynamical Systems 157
SECTION 1. Global Stability of Equilibrium Points 158
1. Banach contraction principle 158
2. Gradient maps 161
3. Triangular maps 163
SECTION 2. Sinks 166
SECTION 3. Repellers and Saddles 172
1. Repelling states 172
2. Saddles 176
SECTION 4. Bounded Invariant Sets 179
1. Dissipative maps 179
2. Quasi bounded maps 182
SECTION 5. Bifurcation 184
1. Bifurcation from the parameter space 185
2. Bifurcation from the state space 188
3. Hopf bifurcation 191
PROBLEMS 193
Contents
CHAPTER 6. Chaotic Behavior 199
SECTION 1. Attractors 200
SECTION 2. Chaotic Dynamical Systems 205
1. Stable and unstable orbits 205
2. Chaotic systems 207
SECTION 3. Dimension 221
1. Capacity and Hausdorff dimension 221
2. Correlation dimension 223
SECTION 4. Lyapunov Exponents 230
PROBLEMS 239
CHAPTER 7. Analysis of four Dynamical Systems 245
SECTION 1. A Blood Cell Population Model 246
SECTION 2. Predator Prey Models 251
SECTION 3. The Lorenz Model 258
SECTION 4. Neural Networks 265
PROBLEMS 270
REFERENCES 275
INDEX 279
|
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| author_facet | Martelli, Mario 1937- |
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| building | Verbundindex |
| bvnumber | BV008267504 |
| classification_rvk | SK 950 |
| classification_tum | MAT 344f MAT 587f |
| ctrlnum | (OCoLC)889286051 (DE-599)BVBBV008267504 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV008267504 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:17:27Z |
| institution | BVB |
| isbn | 0582096375 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005461311 |
| oclc_num | 889286051 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-91 DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-634 DE-188 |
| physical | 282 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Longman Scientific & Technical Wiley |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Martelli, Mario 1937- Verfasser (DE-588)138611092 aut Discrete dynamical systems and chaos Mario Martelli 1. publ. Harlow Longman Scientific & Technical 1992 New York Wiley 282 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 62 Chaotisches System (DE-588)4316104-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Diskretes System (DE-588)4401225-1 s Dynamisches System (DE-588)4013396-5 s Chaotisches System (DE-588)4316104-2 s DE-604 Chaostheorie (DE-588)4009754-7 s DE-188 Pitman monographs and surveys in pure and applied mathematics 62 (DE-604)BV000022446 62 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005461311&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martelli, Mario 1937- Discrete dynamical systems and chaos Pitman monographs and surveys in pure and applied mathematics Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4013396-5 (DE-588)4401225-1 (DE-588)4009754-7 |
| title | Discrete dynamical systems and chaos |
| title_auth | Discrete dynamical systems and chaos |
| title_exact_search | Discrete dynamical systems and chaos |
| title_full | Discrete dynamical systems and chaos Mario Martelli |
| title_fullStr | Discrete dynamical systems and chaos Mario Martelli |
| title_full_unstemmed | Discrete dynamical systems and chaos Mario Martelli |
| title_short | Discrete dynamical systems and chaos |
| title_sort | discrete dynamical systems and chaos |
| topic | Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Chaotisches System Dynamisches System Diskretes System Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005461311&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT martellimario discretedynamicalsystemsandchaos |