Complex and adaptive dynamical systems: a primer ; with 10 tables
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Springer complexity
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 250 S. Ill., graph. Darst. |
| ISBN: | 9783540718734 9783540718741 |
Staff View
MARC
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| 020 | |a 9783540718734 |9 978-3-540-71873-4 | ||
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| 245 | 1 | 0 | |a Complex and adaptive dynamical systems |b a primer ; with 10 tables |c Claudius Gros |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a 250 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer complexity | |
| 650 | 4 | |a Adaptive control systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804137776293085184 |
|---|---|
| adam_text | Contents
Graph Theory and Small-World Networks
........................ 1
1.1
Random Graphs
............................................ 1
1.1.1
The Small-World Effect
............................... 1
1.1.2
Basic Graph-Theoretical Concepts
...................... 3
1.1.3
Properties of Random Graphs
.......................... 7
1.2
Generalized Random Graphs
................................. 11
1.2.1
Graphs with Arbitrary Degree Distributions
.............. 11
1.2.2
Probability Generating Function Formalism
.............. 15
1.2.3
Distribution of Component Sizes
....................... 17
1.3
Robustness of Random Networks
............................. 20
1.4
Small-World Models
........................................ 23
1.5
Scale-Free Graphs
.......................................... 26
Exercises
...................................................... 31
Further Reading
................................................ 31
Chaos, Bifurcations and Diffusion
................................ 33
2.1
Basic Concepts of Dynamical Systems Theory
.................. 33
2.2
The Logistic Map and Deterministic Chaos
..................... 38
2.3
Dissipation and Adaption
.................................... 43
2.3.1
Dissipative Systems and Strange Attractors
.............. 43
2.3.2
Adaptive Systems
.................................... 47
2.4
Diffusion and Transport
..................................... 51
2.4.1
Random Walks, Diffusion and Levy Flights
.............. 52
2.4.2
The
Langevin
Equation and Diffusion
................... 55
2.5
Noise-Controlled Dynamics
.................................. 57
2.5.1
Stochastic Escape
.................................... 58
2.5.2
Stochastic Resonance
................................. 60
Exercises
...................................................... 63
Further Reading
................................................ 64
Random Boolean Networks
..................................... 67
3.1
Introduction
............................................... 67
3.2
Random Variables and Networks
.............................. 69
3.2.1
Boolean Variables and Graph Topologies
................ 69
3.2.2
Coupling Functions
.................................. 71
3.2.3
Dynamics
.......................................... 72
3.3
The Dynamics of Boolean Networks
.......................... 74
3.3.1
The Flow of Information Through the Network
........... 74
3.3.2
The Mean-Field Phase Diagram
........................ 76
3.3.3
The Bifurcation Phase Diagram
........................ 78
3.3.4
Scale-Free Boolean Networks
.......................... 82
3.4
Cycles and Attractors
....................................... 84
3.4.1
Quenched Boolean Dynamics
.......................... 84
3.4.2
The
К
= 1
Kauffman Network
......................... 86
3.4.3
The
К
= 2
Kauffman Network
......................... 87
3.4.4
The K=N Kauffman Network
......................... 88
3.5
Applications
............................................... 91
3.5.1
Living at the Edge of Chaos
........................... 91
3.5.2
The Yeast Cell Cycle
................................. 92
3.5.3
Application to Neural Networks
........................ 94
Exercises
...................................................... 96
Further Reading
................................................ 97
Cellular Automata and Self-Organized Criticality
................. 99
4.1
The Landau Theory of Phase Transitions
....................... 99
4.2
Criticality in Dynamical Systems
.............................104
4.2.1
1/f Noise
...........................................107
4.3
Cellular Automata
..........................................108
4.3.1
Conway s Game of Life
...............................109
4.3.2
The Forest Fire Model
...............:................110
4.4
The Sandpile Model and Self-Organized Criticality
..............112
4.5
Random Branching Theory
..................................115
4.6
Application to Long-Term Evolution
..........................119
Exercises
......................................................126
Further Reading
................................................127
Statistical Modeling of Darwinian Evolution
......................129
5.1
Introduction
...............................................129
5.2
Mutations and Fitness in a Static Environment
..................131
5.3
Deterministic Evolution
.....................................134
5.3.1
Evolution Equations
..................................135
5.3.2
Beanbag Genetics
-
Evolutions Without Epistasis
.........138
5.3.3
Epistatic Interactions and the Error Catastrophe
...........140
5.4
Finite Populations and Stochastic Escape
.......................144
5.4.1
Strong Selective Pressure and Adaptive Climbing
.........145
5.4.2
Adaptive
Climbing Versus Stochastic Escape
.............148
5.5
Prebiotic Evolution
.........................................149
5.5.1
Quasispecies Theory
.................................149
5.5.2
Hypercycles and Autocatalytic Networks
................151
5.6
Coevolution and Game Theory
...............................154
Exercises
......................................................158
Further Reading
................................................159
6
Synchronization Phenomena
....................................161
6.1
Frequency Locking
.........................................161
6.2
Synchronization of Coupled Oscillators
........................162
6.3
Synchronization of Relaxation Oscillators
......................168
6.4
Synchronization and Object Recognition in Neural Networks
......172
6.5
Synchronization Phenomena in Epidemics
......................175
Exercises
......................................................178
Further Reading
................................................179
7
Elements of Cognitive Systems Theory
...........................181
7.1
Introduction
...............................................181
7.2
Foundations of Cognitive Systems Theory
......................183
7.2.1
Basic Requirements for the Dynamics
...................183
7.2.2
Cognitive Information Processing Versus Diffusive Control
. 187
7.2.3
Basic Layout Principles
...............................189
7.2.4
Learning and Memory Representations
..................191
7.3
Motivation, Benchmarks and Target-Oriented Self-Organization
... 195
7.3.1
Cognitive Tasks
.....................................195
7.3.2
Internal Benchmarks
.................................196
7.4
Competitive Dynamics and Winning Coalitions
.................199
7.4.1
General Considerations
...............................199
7.4.2
Associative Thought Processes
.........................203
7.4.3
Autonomous Online Learning
..........................207
7.5
Environmental Model Building
...............................211
7.5.1
The Elman Simple Recurrent Network
..................211
7.5.2
Universal Prediction Tasks
............................215
Exercises
......................................................218
Further Reading
................................................218
8
Solutions
......................................................221
Index
.............................................................241
|
| adam_txt |
Contents
Graph Theory and Small-World Networks
. 1
1.1
Random Graphs
. 1
1.1.1
The Small-World Effect
. 1
1.1.2
Basic Graph-Theoretical Concepts
. 3
1.1.3
Properties of Random Graphs
. 7
1.2
Generalized Random Graphs
. 11
1.2.1
Graphs with Arbitrary Degree Distributions
. 11
1.2.2
Probability Generating Function Formalism
. 15
1.2.3
Distribution of Component Sizes
. 17
1.3
Robustness of Random Networks
. 20
1.4
Small-World Models
. 23
1.5
Scale-Free Graphs
. 26
Exercises
. 31
Further Reading
. 31
Chaos, Bifurcations and Diffusion
. 33
2.1
Basic Concepts of Dynamical Systems Theory
. 33
2.2
The Logistic Map and Deterministic Chaos
. 38
2.3
Dissipation and Adaption
. 43
2.3.1
Dissipative Systems and Strange Attractors
. 43
2.3.2
Adaptive Systems
. 47
2.4
Diffusion and Transport
. 51
2.4.1
Random Walks, Diffusion and Levy Flights
. 52
2.4.2
The
Langevin
Equation and Diffusion
. 55
2.5
Noise-Controlled Dynamics
. 57
2.5.1
Stochastic Escape
. 58
2.5.2
Stochastic Resonance
. 60
Exercises
. 63
Further Reading
. 64
Random Boolean Networks
. 67
3.1
Introduction
. 67
3.2
Random Variables and Networks
. 69
3.2.1
Boolean Variables and Graph Topologies
. 69
3.2.2
Coupling Functions
. 71
3.2.3
Dynamics
. 72
3.3
The Dynamics of Boolean Networks
. 74
3.3.1
The Flow of Information Through the Network
. 74
3.3.2
The Mean-Field Phase Diagram
. 76
3.3.3
The Bifurcation Phase Diagram
. 78
3.3.4
Scale-Free Boolean Networks
. 82
3.4
Cycles and Attractors
. 84
3.4.1
Quenched Boolean Dynamics
. 84
3.4.2
The
К
= 1
Kauffman Network
. 86
3.4.3
The
К
= 2
Kauffman Network
. 87
3.4.4
The K=N Kauffman Network
. 88
3.5
Applications
. 91
3.5.1
Living at the Edge of Chaos
. 91
3.5.2
The Yeast Cell Cycle
. 92
3.5.3
Application to Neural Networks
. 94
Exercises
. 96
Further Reading
. 97
Cellular Automata and Self-Organized Criticality
. 99
4.1
The Landau Theory of Phase Transitions
. 99
4.2
Criticality in Dynamical Systems
.104
4.2.1
1/f Noise
.107
4.3
Cellular Automata
.108
4.3.1
Conway's Game of Life
.109
4.3.2
The Forest Fire Model
.:.110
4.4
The Sandpile Model and Self-Organized Criticality
.112
4.5
Random Branching Theory
.115
4.6
Application to Long-Term Evolution
.119
Exercises
.126
Further Reading
.127
Statistical Modeling of Darwinian Evolution
.129
5.1
Introduction
.129
5.2
Mutations and Fitness in a Static Environment
.131
5.3
Deterministic Evolution
.134
5.3.1
Evolution Equations
.135
5.3.2
Beanbag Genetics
-
Evolutions Without Epistasis
.138
5.3.3
Epistatic Interactions and the Error Catastrophe
.140
5.4
Finite Populations and Stochastic Escape
.144
5.4.1
Strong Selective Pressure and Adaptive Climbing
.145
5.4.2
Adaptive
Climbing Versus Stochastic Escape
.148
5.5
Prebiotic Evolution
.149
5.5.1
Quasispecies Theory
.149
5.5.2
Hypercycles and Autocatalytic Networks
.151
5.6
Coevolution and Game Theory
.154
Exercises
.158
Further Reading
.159
6
Synchronization Phenomena
.161
6.1
Frequency Locking
.161
6.2
Synchronization of Coupled Oscillators
.162
6.3
Synchronization of Relaxation Oscillators
.168
6.4
Synchronization and Object Recognition in Neural Networks
.172
6.5
Synchronization Phenomena in Epidemics
.175
Exercises
.178
Further Reading
.179
7
Elements of Cognitive Systems Theory
.181
7.1
Introduction
.181
7.2
Foundations of Cognitive Systems Theory
.183
7.2.1
Basic Requirements for the Dynamics
.183
7.2.2
Cognitive Information Processing Versus Diffusive Control
. 187
7.2.3
Basic Layout Principles
.189
7.2.4
Learning and Memory Representations
.191
7.3
Motivation, Benchmarks and Target-Oriented Self-Organization
. 195
7.3.1
Cognitive Tasks
.195
7.3.2
Internal Benchmarks
.196
7.4
Competitive Dynamics and Winning Coalitions
.199
7.4.1
General Considerations
.199
7.4.2
Associative Thought Processes
.203
7.4.3
Autonomous Online Learning
.207
7.5
Environmental Model Building
.211
7.5.1
The Elman Simple Recurrent Network
.211
7.5.2
Universal Prediction Tasks
.215
Exercises
.218
Further Reading
.218
8
Solutions
.221
Index
.241 |
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| author | Gros, Claudius 1961- |
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| discipline_str_mv | Physik Informatik |
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| id | DE-604.BV023396143 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:21:53Z |
| indexdate | 2024-07-09T21:17:40Z |
| institution | BVB |
| isbn | 9783540718734 9783540718741 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016579006 |
| oclc_num | 227005909 |
| open_access_boolean | |
| owner | DE-20 DE-739 DE-83 DE-19 DE-BY-UBM DE-473 DE-BY-UBG |
| owner_facet | DE-20 DE-739 DE-83 DE-19 DE-BY-UBM DE-473 DE-BY-UBG |
| physical | 250 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer complexity |
| spelling | Gros, Claudius 1961- Verfasser (DE-588)134168461 aut Complex and adaptive dynamical systems a primer ; with 10 tables Claudius Gros Berlin [u.a.] Springer 2008 250 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer complexity Adaptive control systems Differentiable dynamical systems 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 DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016579006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gros, Claudius 1961- Complex and adaptive dynamical systems a primer ; with 10 tables Adaptive control systems Differentiable dynamical systems 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 ; with 10 tables |
| title_auth | Complex and adaptive dynamical systems a primer ; with 10 tables |
| title_exact_search | Complex and adaptive dynamical systems a primer ; with 10 tables |
| title_exact_search_txtP | Complex and adaptive dynamical systems a primer ; with 10 tables |
| title_full | Complex and adaptive dynamical systems a primer ; with 10 tables Claudius Gros |
| title_fullStr | Complex and adaptive dynamical systems a primer ; with 10 tables Claudius Gros |
| title_full_unstemmed | Complex and adaptive dynamical systems a primer ; with 10 tables Claudius Gros |
| title_short | Complex and adaptive dynamical systems |
| title_sort | complex and adaptive dynamical systems a primer with 10 tables |
| title_sub | a primer ; with 10 tables |
| topic | Adaptive control systems Differentiable dynamical systems Komplexes System (DE-588)4114261-5 gnd Dynamisches System (DE-588)4013396-5 gnd Adaptives System (DE-588)4247928-9 gnd |
| topic_facet | Adaptive control systems Differentiable dynamical systems Komplexes System Dynamisches System Adaptives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016579006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grosclaudius complexandadaptivedynamicalsystemsaprimerwith10tables |