Adaptive coevolutionary networks: a review
Thilo Gross,Bernd Blasius +1 more
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TLDR
It is demonstrated that all these studies investigating the dynamics of adaptive networks are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.Abstract:
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.read more
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Statistical physics of social dynamics
TL;DR: In this article, a wide list of topics ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading are reviewed and connections between these problems and other, more traditional, topics of statistical physics are highlighted.
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Epidemic processes in complex networks
TL;DR: A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear.
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Synchronization in complex networks
Alex Arenas,Alex Arenas,Albert Díaz-Guilera,Albert Díaz-Guilera,Jürgen Kurths,Jürgen Kurths,Yamir Moreno,Changsong Zhou +7 more
TL;DR: The advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology are reported and the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections are overviewed.
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Temporal Networks
Petter Holme,Jari Saramäki +1 more
TL;DR: This review presents the emergent field of temporal networks, and discusses methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems.
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Critical phenomena in complex networks
TL;DR: A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolations, phenomena near epidemic thresholds, condensation transitions,critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned.
References
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Collective dynamics of small-world networks
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
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Emergence of Scaling in Random Networks
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
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The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
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Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.