Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur.Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Sol shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies.Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.
Author(s): Ricard V. Sole
Publisher: Princeton University Press
Year: 2011
Language: English
Pages: 238
Tags: Биологические дисциплины;Матметоды и моделирование в биологии;
Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 12
1.1 Complexity......Page 16
1.2 Phase diagrams......Page 19
1.3 Interactions make a difference......Page 22
1.4 The Ising model: From micro to macro......Page 26
1.5 Monte Carlo simulation......Page 28
1.6 Scaling and universality......Page 32
1.7 Mean field Ising model......Page 33
1.8 Nonequilibrium transitions......Page 38
2.1 Dynamical systems......Page 40
2.2 Attractors......Page 42
2.3 Nonlinear dynamics......Page 45
2.4 Linear stability analysis......Page 48
3.1 Qualitative changes......Page 52
3.2 Symmetry breaking......Page 53
3.3 Catastrophes and breakpoints......Page 59
3.4 Critical slowing down......Page 64
3.5 Multiple broken symmetries......Page 66
4.1 Systems are connected......Page 68
4.2 Percolation thresholds......Page 69
4.3 Percolation is widespread......Page 72
4.4 Bethe lattices......Page 74
5.1 The Erdos-Renyi model......Page 78
5.2 Statistical patterns......Page 79
5.3 Percolation at critical connectivity......Page 80
5.4 Real networks are heterogeneous......Page 83
6.1 Prebiotic evolution......Page 85
6.2 Replicators and reproducers......Page 86
6.3 Autocatalysis and cooperation......Page 87
6.4 Prebiotic reaction networks......Page 90
7.1 Molecular parasites......Page 93
7.2 Exploring the hypercube......Page 95
7.3 Swetina-Schuster quasispecies model......Page 99
7.4 Critical genome size......Page 102
7.5 Beyond the threshold......Page 103
8.1 The architecture of cells......Page 106
8.2 States and transitions......Page 109
8.3 Dynamical instability model......Page 110
8.4 Tensegrity......Page 112
9.1 Spreading diseases......Page 114
9.2 SIS model......Page 117
9.3 Vaccination thresholds......Page 120
9.4 Pathogens and networks......Page 122
10.1 Genes and cell types......Page 124
10.2 Boolean dynamics......Page 127
10.3 Percolation analysis......Page 128
10.4 Is cell dynamics Boolean?......Page 133
11.1 Abnormal growth......Page 135
11.2 Tumor decay under immune attack......Page 137
11.3 Thresholds in cancer instability......Page 143
11.4 Cancer as an evolving system......Page 147
12.1 Change in ecology......Page 149
12.2 Green-desert transitions......Page 151
12.3 Continuous transitions......Page 153
12.4 Sudden shifts......Page 155
12.5 Metapopulation dynamics......Page 158
12.6 Warning signals......Page 161
13.1 Internet and computer networks......Page 163
13.2 Mean field model of traffic flow......Page 165
13.3 Fluid flow and congestion explosion......Page 167
13.4 Self-regulated traffic......Page 169
14.1 Swarm behavior......Page 172
14.2 Foraging and broken symmetry......Page 174
14.3 Order-disorder transitions in ant colonies......Page 177
14.4 Structure and evolution in social insects......Page 180
15.1 Lexical change......Page 182
15.2 Words: Birth and death......Page 184
15.3 String models......Page 186
15.4 Symmetric model......Page 189
15.5 Language thresholds......Page 191
16.1 Rise and fall......Page 194
16.2 Slow responses and sunk-cost effects......Page 196
16.3 Ecological model of social collapse......Page 197
16.4 Historical dynamics......Page 201
References......Page 204
Index......Page 230
