Modeling complex systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 489 S. Ill., graph. Darst. |
| ISBN: | 9781461426813 9781441965615 |
Internformat
MARC
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| 100 | 1 | |a Boccara, Nino |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modeling complex systems |c Nino Boccara |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a XVII, 489 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Graduate texts in physics | |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020664133 | ||
Datensatz im Suchindex
| _version_ | 1804143407194439680 |
|---|---|
| adam_text | Contents
Preface
of the First Edition
...................................
vii
Preface of the Second Edition
................................. ix
Notations
...................................................... xv
1
Introduction
............................................... 1
1.1
What is a Complex System?
.............................. 2
1.2
What is a Model?
....................................... 6
1.3
What is a Dynamical System?
............................ 11
Exercises
................................................... 18
Solutions
................................................... 19
Summary
................................................... 23
2
How to Build Up a Model
................................. 25
2.1
Lotka-Volterra Model
.................................... 26
2.2
More Realistic Predator-Prey Models
...................... 33
2.3
A Model with a Stable Limit Cycle
........................ 34
2.4
Fluctuating Environments
................................ 36
2.5
Hutchinson s Time-Delay Model
........................... 37
2.6
Discrete-Time Models
.................................... 40
2.7
Lattice Models
.......................................... 41
Exercises
................................................... 45
Solutions
................................................... 46
Summary
................................................... 49
3
Differential Equations
..................................... 53
3.1
Flows
.................................................. 54
3.2
Linearization and Stability
................................ 64
3.2.1
Linear Systems
.................................... 64
3.2.2
Nonlinear Systems
................................. 69
3.3
Graphical Study of Two-Dimensional Systems
............... 79
Contents
3.4
Structural
Stability
...................................... 82
3.5
Local Bifurcations of Vector Fields
........................ 85
3.5.1
One-Dimensional Vector Fields
...................... 86
3.5.2
Equivalent Families of Vector Fields
................. 96
3.5.3 Hopf
Bifurcation
.................................. 97
3.5.4
Catastrophes
.....................................100
3.6
Influence of Diffusion
....................................105
3.6.1
Random Walk and Diffusion
........................106
3.6.2
One-Population Dynamics with Dispersal
.............107
3.6.3
Critical Patch Size
.................................108
3.6.4
Diffusion-Induced Instability
........................110
Exercises
...................................................113
Solutions
...................................................115
Summary
...................................................123
Recurrence Equations
.....................................127
4.1
Iteration of Maps
........................................127
4.2
Stability
................................................130
4.3
Poincaré
Maps
..........
і
................................138
4.4
Local Bifurcations of Maps
...............................140
4.4.1
Maps on
R
.......................................141
4.4.2
The
Hopf
Bifurcation
..............................146
4.5
Sequences of Period-Doubling Bifurcations
..................148
4.5.1
Logistic Model
....................................148
4.5.2
Universality
......................................152
Exercises
...................................................157
Solutions
...................................................160
Summary
...................................................167
Chaos
.....................................................171
5.1
Defining Chaos
..........................................174
5.1.1
Dynamics of the Logistic Map
/4....................176
5.1.2
Definition of Chaos
................................180
5.2
Routes to Chaos
.........................................181
5.3
Characterizing Chaos
....................................183
5.3.1
Stochastic Properties
..............................183
5.3.2
Lyapunov Exponent
...............................185
5.3.3
Period Three Implies Chaos
......................186
5.3.4
Strange Attractors
.................................188
5.4
Chaotic Discrete-Time Models
............................197
5.4.1
One-Population Models
............................197
5.4.2
The
Hénon Map
...................................199
5.5
Chaotic Continuous-Time Models
..........................202
5.5.1
The
Lorenz
Model
.................................202
Contents xiii
Exercises
...................................................204
Solutions ...................................................206
Summary
...................................................214
Spatial Models
............................................219
6.1
Cellular Automata
.......................................220
6.2
Number-Conserving Cellular Automata
....................223
6.3
Eventually Number-Conserving Cellular Automata
..........237
6.4
Approximate Methods
...................................240
6.5
Generalized Cellular Automata
............................247
6.6
Kinetic Growth Phenomena
...............................253
6.7
Site-Exchange Cellular Automata
..........................261
6.8
Agent-Based Spatial Models
..............................276
6.9
Sociophysics
............................................278
Exercises
...................................................299
Solutions
...................................................303
Summary
...................................................318
Networks
..................................................325
7.1
The Small-World Phenomenon
............................325
7.2
Graphs
.................................................327
7.3
Random Networks
.......................................331
7.4
Small-World Networks
...................................335
7.4.1
Watts-Strogatz Model
.............................335
7.4.2
Newman-Watts Model
.............................338
7.4.3
Highly Connected Extra Vertex Model
...............339
7.5
Scale-Free Networks
.....................................339
7.5.1
Empirical Results
.................................339
7.5.2
A Few Models
....................................344
Exercises
...................................................350
Solutions
...................................................353
Summary
...................................................364
Power-Law Distributions
..................................371
8.1
Classical Examples
......................................371
8.2
A Few Notions of Probability Theory
......................378
8.2.1
Basic Definitions
..................................378
8.2.2
Central Limit Theorem
............................382
8.2.3 Lognormal
Distribution
............................386
8.2.4
Levy Distributions
.................................387
8.2.5
Truncated Levy Distributions
.......................391
8.2.6
Student s i-Distribution
............................392
8.2.7
A Word About Statistics
...........................394
8.3
Empirical Results and Tentative Models
....................397
8.3.1
Financial Markets
.................................397
xiv Contents
8.3.2 Demographic
and Area
Distribution.................401
8.3.3 Family
Names
....................................402
8.3.4 Distribution
of Votes...............................
403
8.4
Self-Organized Criticality
.................................404
8.4.1 The Sandpile Model...............................404
8.4.2 Drossel-Schwabl
Forest Fire
Model..................405
8.4.3
Punctuated Equilibria and Darwinian Evolution
.......407
8.4.4
Real-Life Phenomena
..............................409
Exercises
...................................................414
Solutions
...................................................417
Summary
...................................................430
Glossary
.......................................................435
References
.....................................................459
Index
..........................................................481
|
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| id | DE-604.BV036746791 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:47:10Z |
| institution | BVB |
| isbn | 9781461426813 9781441965615 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020664133 |
| oclc_num | 700441595 |
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| physical | XVII, 489 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
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| series2 | Graduate texts in physics |
| spelling | Boccara, Nino Verfasser aut Modeling complex systems Nino Boccara 2. ed. New York [u.a.] Springer 2010 XVII, 489 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Komplexes System (DE-588)4114261-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Komplexes System (DE-588)4114261-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020664133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boccara, Nino Modeling complex systems Komplexes System (DE-588)4114261-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4114528-8 |
| title | Modeling complex systems |
| title_auth | Modeling complex systems |
| title_exact_search | Modeling complex systems |
| title_full | Modeling complex systems Nino Boccara |
| title_fullStr | Modeling complex systems Nino Boccara |
| title_full_unstemmed | Modeling complex systems Nino Boccara |
| title_short | Modeling complex systems |
| title_sort | modeling complex systems |
| topic | Komplexes System (DE-588)4114261-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Komplexes System Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020664133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boccaranino modelingcomplexsystems |