Complex and adaptive dynamical systems: a primer
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Springer complexity
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIV, 345 S. Ill., graph. Darst. |
| ISBN: | 364236585X 9783642365850 |
Internformat
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| 245 | 1 | 0 | |a Complex and adaptive dynamical systems |b a primer |c Claudius Gros |
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIV, 345 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text |
CONTENTS
1 GRAPH THEORY AND SMALL-WORLD NETWORKS 1
1.1 GRAPH THEORY AND REAL-WORLD NETWORKS 1
1.1.1 THE SMALL-WORLD EFFECT 1
1.1.2 BASIC GRAPH-THEORETICAL CONCEPTS 3
1.1.3 GRAPH SPECTRA AND DEGREE DISTRIBUTIONS 8
1.2 PERCOLATION IN GENERALIZED RANDOM GRAPHS 14
1.2.1 GRAPHS WITH ARBITRARY DEGREE DISTRIBUTIONS 15
1.2.2 PROBABILITY GENERATING FUNCTION FORMALISM 20
1.2.3 DISTRIBUTION OF COMPONENT SIZES 22
1.3 ROBUSTNESS OF RANDOM NETWORKS 26
1.4 SMALL-WORLD MODELS 30
1.5 SCALE-FREE GRAPHS 32
EXERCISES 37
FURTHER READING 39
REFERENCES 39
2 CHAOS, BIFURCATIONS AND DIFFUSION 41
2.1 BASIC CONCEPTS OF DYNAMICAL SYSTEMS THEORY 41
2.2 BIFURCATIONS AND STABILITY 47
2.3 THE LOGISTIC MAP AND DETERMINISTIC CHAOS 51
2.4 DISSIPATION AND ADAPTION 56
2.4.1 DISSIPATIVE SYSTEMS AND STRANGE ATTRACTORS 57
2.4.2 ADAPTIVE SYSTEMS 61
2.5 DIFFUSION AND TRANSPORT 66
2.5.1 RANDOM WALKS, DIFFUSION AND LEVY FLIGHTS 66
2.5.2 THE LANGEVIN EQUATION AND DIFFUSION 69
2.6 NOISE-CONTROLLED DYNAMICS 71
2.6.1 STOCHASTIC ESCAPE 72
2.6.2 STOCHASTIC RESONANCE 75
2.7 DYNAMICAL SYSTEMS WITH TIME DELAYS 78
VII
HTTP://D-NB.INFO/1030170177
VIII CONTENTS
EXERCISES 81
FURTHER READING 82
REFERENCES 83
3 COMPLEXITY AND INFORMATION THEORY 85
3.1 PROBABILITY DISTRIBUTION FUNCTIONS 85
3.1.1 BAYESIAN STATISTICS 88
3.1.2 THE LAW OF LARGE NUMBERS 91
3.1.3 TIME SERIES CHARACTERIZATION 92
3.2 ENTROPY AND INFORMATION 96
3.2.1 INFORMATION CONTENT OF A REAL-WORLD TIME SERIES 102
3.2.2 MUTUAL INFORMATION 103
3.2.3 KULLBACK-LEIBLER DIVERGENCE 108
3.3 COMPLEXITY MEASURES 110
3.3.1 COMPLEXITY AND PREDICTABILITY 112
3.3.2 ALGORITHMIC AND GENERATIVE COMPLEXITY 114
EXERCISES 116
FURTHER READING 118
REFERENCES 118
4 RANDOM BOOLEAN NETWORKS 121
4.1 INTRODUCTION 121
4.2 RANDOM VARIABLES AND NETWORKS 123
4.2.1 BOOLEAN VARIABLES AND GRAPH TOPOLOGIES 123
4.2.2 COUPLING FUNCTIONS 125
4.2.3 DYNAMICS 127
4.3 THE DYNAMICS OF BOOLEAN NETWORKS 128
4.3.1 THE FLOW OF INFORMATION THROUGH THE NETWORK 129
4.3.2 THE MEAN-FIELD PHASE DIAGRAM 131
4.3.3 THE BIFURCATION PHASE DIAGRAM 133
4.3.4 SCALE-FREE BOOLEAN NETWORKS 137
4.4 CYCLES AND ATTRACTORS 139
4.4.1 QUENCHED BOOLEAN DYNAMICS 139
4.4.2 THE K = 1 KAUFFMAN NETWORK 142
4.4.3 THE K = 2 KAUFFMAN NETWORK 144
4.4.4 THE K = N KAUFFMAN NETWORK 145
4.5 APPLICATIONS 147
4.5.1 LIVING AT THE EDGE OF CHAOS 147
4.5.2 THE YEAST CELL CYCLE 149
4.5.3 APPLICATION TO NEURAL NETWORKS 151
EXERCISES 153
FURTHER READING 154
REFERENCES 154
CONTENTS IX
5 CELLULAR AUTOMATA AND SELF-ORGANIZED CRITICALITY 157
5.1 THE LANDAU THEORY OF PHASE TRANSITIONS 157
5.2 CRITICALITY IN DYNAMICAL SYSTEMS 162
5.2.1 1/F NOISE 166
5.3 CELLULAR AUTOMATA 167
5.3.1 CONWAY'S GAME OF LIFE 168
5.3.2 THE FOREST FIRE MODEL 169
5.4 THE SANDPILE MODEL AND SELF-ORGANIZED CRITICALITY 171
5.4.1 ABSORBING PHASE TRANSITIONS 173
5.5 RANDOM BRANCHING THEORY 175
5.5.1 BRANCHING THEORY OF SELF-ORGANIZED CRITICALITY 175
5.5.2 GALTON-WATSON PROCESSES 180
5.6 APPLICATION TO LONG-TERM EVOLUTION 182
EXERCISES 188
FURTHER READING 189
REFERENCES 190
6 DARWINIAN EVOLUTION, HYPERCYCLES AND GAME THEORY 191
6.1 INTRODUCTION 191
6.2 MUTATIONS AND FITNESS IN A STATIC ENVIRONMENT 193
6.3 DETERMINISTIC EVOLUTION 197
6.3.1 EVOLUTION EQUATIONS 197
6.3.2 BEANBAG GENETICS: EVOLUTIONS WITHOUT EPISTASIS 200
6.3.3 EPISTATIC INTERACTIONS AND THE ERROR CATASTROPHE 202
6.4 FINITE POPULATIONS AND STOCHASTIC ESCAPE 206
6.4.1 STRONG SELECTIVE PRESSURE AND ADAPTIVE CLIMBING 207
6.4.2 ADAPTIVE CLIMBING VERSUS STOCHASTIC ESCAPE 210
6.5 PREBIOTIC EVOLUTION 212
6.5.1 QUASISPECIES THEORY 212
6.5.2 HYPERCYCLES AND AUTOCATALYTIC NETWORKS 213
6.6 MACROECOLOGY AND SPECIES COMPETITION 217
6.7 COEVOLUTION AND GAME THEORY 220
EXERCISES 225
FURTHER READING 226
REFERENCES 227
7 SYNCHRONIZATION PHENOMENA 229
7.1 FREQUENCY LOCKING 229
7.2 SYNCHRONIZATION OF COUPLED OSCILLATORS 230
7.3 SYNCHRONIZATION WITH TIME DELAYS 237
7.4 SYNCHRONIZATION VIA AGGREGATE AVERAGING 239
7.5 SYNCHRONIZATION VIA CAUSAL SIGNALING 243
7.6 SYNCHRONIZATION AND OBJECT RECOGNITION IN NEURAL NETWORKS 246
7.7 SYNCHRONIZATION PHENOMENA IN EPIDEMICS 250
X
CONTENTS
EXERCISES 253
FURTHER READING 254
REFERENCES 255
8 ELEMENTS OF COGNITIVE SYSTEMS THEORY 257
8.1 INTRODUCTION 257
8.2 FOUNDATIONS OF COGNITIVE SYSTEMS THEORY 260
8.2.1 BASIC REQUIREMENTS FOR THE DYNAMICS 260
8.2.2 COGNITIVE INFORMATION PROCESSING VERSUS
DIFFUSIVE CONTROL 263
8.2.3 BASIC LAYOUT PRINCIPLES 266
8.2.4 LEARNING AND MEMORY REPRESENTATIONS 267
8.3 POLYHOMEOSTASIS AND DIFFUSIVE EMOTIONAL CONTROL 271
8.3.1 METALEARNING THROUGH POLYHOMEOSTASIS 272
8.3.2 EMOTIONAL AND NEUTRAL DIFFUSIVE CONTROL 274
8.4 COMPETITIVE DYNAMICS AND WINNING COALITIONS 276
8.4.1 GENERAL CONSIDERATIONS 276
8.4.2 ASSOCIATIVE THOUGHT PROCESSES 281
8.4.3 AUTONOMOUS ONLINE LEARNING 285
8.5 ENVIRONMENTAL MODEL BUILDING 287
8.5.1 THE ELMAN SIMPLE RECURRENT NETWORK 287
8.5.2 UNIVERSAL PREDICTION TASKS 292
EXERCISES 294
FURTHER READING 295
REFERENCES 296
9 SOLUTIONS 299
9.1 SOLUTIONS TO THE EXERCISES OF CHAPTER 1 299
9.2 SOLUTIONS TO THE EXERCISES OF CHAPTER 2 306
9.3 SOLUTIONS TO THE EXERCISES OF CHAPTER 3 310
9.4 SOLUTIONS TO THE EXERCISES OF CHAPTER 4 316
9.5 SOLUTIONS TO THE EXERCISES OF CHAPTER 5 320
9.6 SOLUTIONS TO THE EXERCISES OF CHAPTER 6 325
9.7 SOLUTIONS TO THE EXERCISES OF CHAPTER 7 329
9.8 SOLUTIONS TO THE EXERCISES OF CHAPTER 8 332
INDEX 335
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All calculations are presented step by step and are straightforward
tö
follow This new
third edition
coroes
With new material, figures and exercises.
.
Network theory, dynamical systems arid
infoiinątion
theory, the core of modern
complex system sciences, are developed in the first three chapters, covering basic con-
cepţs
and phenomena like small-world networks* bifurcation theory and information
entropy.
.
Further chapters use a modular approach to address the most important concepts in
complex system sciences, with the emergence and self-organization playing a central
role. Prominent examples are self-organized criticality in adaptive systems, life at the
edge of chaos, hypercycles and
coe
volution
ary
avalanches, synchronization phenom¬
ena, absorbing phase transitions and the cognitive system approach to the brain.
Technical course prerequisites are the standard mathematical tools for an advanced
undergraduate course in the natural sciences or engineering. Each chapter comes with
exercises and suggestions for further reading
-
solutions to the exercises are provided
in the last chapter. |
| any_adam_object | 1 |
| author | Gros, Claudius 1961- |
| author_GND | (DE-588)134168461 |
| author_facet | Gros, Claudius 1961- |
| author_role | aut |
| author_sort | Gros, Claudius 1961- |
| author_variant | c g cg |
| building | Verbundindex |
| bvnumber | BV041441097 |
| classification_rvk | UG 3900 |
| ctrlnum | (OCoLC)852546617 (DE-599)BVBBV041441097 |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV041441097 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:05:31Z |
| institution | BVB |
| isbn | 364236585X 9783642365850 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026887871 |
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| owner_facet | DE-19 DE-BY-UBM DE-739 |
| physical | XIV, 345 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
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| spelling | Gros, Claudius 1961- Verfasser (DE-588)134168461 aut Complex and adaptive dynamical systems a primer Claudius Gros 3. ed. Berlin [u.a.] Springer 2013 XIV, 345 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer complexity Komplexes System (DE-588)4114261-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Adaptives System (DE-588)4247928-9 gnd rswk-swf Komplexes System (DE-588)4114261-5 s Adaptives System (DE-588)4247928-9 s Dynamisches System (DE-588)4013396-5 s 1\p DE-604 DE-604 Erscheint auch als Online-Ausgabe 978-3-642-36586-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4242514&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026887871&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026887871&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gros, Claudius 1961- Complex and adaptive dynamical systems a primer Komplexes System (DE-588)4114261-5 gnd Dynamisches System (DE-588)4013396-5 gnd Adaptives System (DE-588)4247928-9 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4013396-5 (DE-588)4247928-9 |
| title | Complex and adaptive dynamical systems a primer |
| title_auth | Complex and adaptive dynamical systems a primer |
| title_exact_search | Complex and adaptive dynamical systems a primer |
| title_full | Complex and adaptive dynamical systems a primer Claudius Gros |
| title_fullStr | Complex and adaptive dynamical systems a primer Claudius Gros |
| title_full_unstemmed | Complex and adaptive dynamical systems a primer Claudius Gros |
| title_short | Complex and adaptive dynamical systems |
| title_sort | complex and adaptive dynamical systems a primer |
| title_sub | a primer |
| topic | Komplexes System (DE-588)4114261-5 gnd Dynamisches System (DE-588)4013396-5 gnd Adaptives System (DE-588)4247928-9 gnd |
| topic_facet | Komplexes System Dynamisches System Adaptives System |
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