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Zusatztext "Mean-field approaches constitute an elegant and considerable contribution to complex systems studies, and I commend Sole for his rigorous presentation." ---Lael Parrott, BioScience Informationen zum Autor Ricard V. Solé is research professor and head of the Complex Systems Lab at Pompeu Fabra University and external professor at the Santa Fe Institute. He is the coauthor of Signs of Life (Basic) and Self-Organization in Complex Ecosystems (Princeton). Klappentext "This ambitious book provides an elegant and much-needed synthesis to many of the ideas that have come to define the field of complex systems and their applications to nature and society. It makes an important contribution to the field, especially for researchers and students looking for an overview of the literature and entry points for research." --Luis Bettencourt, Los Alamos National Laboratory and the Santa Fe Institute "This clear and easy-to-follow book is a valuable compilation of systems showing phase transition phenomena that have become more and more important in understanding natural and man-made complex systems. It is a useful addition to the already existing literature." --Stefan Thurner, Medical University of Vienna Zusammenfassung 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 Solé 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. Inhaltsverzeichnis Preface xi Chapter 1. Phase Changes 1 1.1 Complexity 1 1.2 Phase diagrams 4 1.3 Interactions make a difference 7 1.4 The Ising model: From micro to macro 11 1.5 Monte Carlo simulation 13 1.6 Scaling and universality 17 1.7 Mean field Ising model 18 1.8 Nonequilibrium transitions 23 Chapter 2. Stability and Instability 25 2.1 Dynamical systems 25 2.2 Attractors 27 2.3 Nonlinear dynamics 30 2.4 Linear stability analysis 33 Chapter 3. Bifurcations and Catastrophes 37 3.1 Qualitative changes 37 3.2 Symmetry breaking 38 3.3 Catastrophes and breakpoints 43 3.4 Critical slowing down 49 3.5 Multiple broken symmetries 51 Chapter 4. Percolation 53 4.1 Systems are connected 53 4.2 Percolation thresholds 54 4.3 Percolation is widespread 57 4.4 Bethe lattices 59 Chapter 5. Random Graphs 63 5.1 The Erdos-Renyi model 63 5.2 Statistical patterns 64 5.3 Percolation at critical connectivity 65 5.4 Real networks are heterogeneous 68 Chapter 6. Life Origins 70 6.1 Prebiotic evolution 70 6.2 Replicators and reproducers 71 6.3 Autocatalysis and cooperation 72 6.4 Prebiotic reaction networks 75 Chapter 7. Virus Dynamics 78 7.1 Molecular parasites 78 7.2 Exploring the hypercube 80 7.3 S...
About the author
Ricard V. Solé is research professor and head of the Complex Systems Lab at Pompeu Fabra University and external professor at the Santa Fe Institute. He is the coauthor of
Signs of Life (Basic) and
Self-Organization in Complex Ecosystems (Princeton).
Summary
Exploring the origins and implications of sudden changes in nature and society, this title examines different dynamical behaviors in a range of complex systems. Using a set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, it reveals how phase transitions occur.
