Networks, Topology and Dynamics
Networks, Topology and Dynamics

Author: Ahmad K. Naimzada

Publisher: Springer Science & Business Media

Published: 2008-11-14

Total Pages: 292

ISBN-13: 3540684093

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There is convergent consensus among scientists that many social, economic and ?nancial phenomena can be described by a network of agents and their inter- tions. Surprisingly, even though the application ?elds are quite different, those n- works often show a common behaviour. Thus, their topological properties can give useful insights on how the network is structured, which are the most “important” nodes/agents, how the network reacts to new arrivals. Moreover the network, once included into a dynamic context, helps to model many phenomena. Among the t- ics in which topology and dynamics are the essential tools, we will focus on the diffusion of technologies and fads, the rise of industrial districts, the evolution of ?nancial markets, cooperation and competition, information ?ows, centrality and prestige. The volume, including recent contributions to the ?eld of network modelling, is based on the communications presented at NET 2006 (Verbania, Italy) and NET 2007 (Urbino, Italy); offers a wide range of recent advances, both theoretical and methodological, that will interest academics as well as practitioners. Theory and applications are nicely integrated: theoretical papers deal with graph theory, game theory, coalitions, dynamics, consumer behavior, segregation models and new contributions to the above mentioned area. The applications cover a wide range: airline transportation, ?nancial markets, work team organization, labour and credit market.

Higher Order Networks: An Introduction to Simplicial Complexes
Higher Order Networks: An Introduction to Simplicial Complexes

Author: Ginestra Bianconi

Publisher: Cambridge University Press

Published: 2021-12-23

Total Pages: 149

ISBN-13: 1108726739

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This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.

Dynamics On and Of Complex Networks
Dynamics On and Of Complex Networks

Author: Niloy Ganguly

Publisher: Springer Science & Business Media

Published: 2009-04-14

Total Pages: 310

ISBN-13: 0817647503

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This self-contained book systematically explores the statistical dynamics on and of complex networks having relevance across a large number of scientific disciplines. The theories related to complex networks are increasingly being used by researchers for their usefulness in harnessing the most difficult problems of a particular discipline. The book is a collection of surveys and cutting-edge research contributions exploring the interdisciplinary relationship of dynamics on and of complex networks. Topics covered include complex networks found in nature—genetic pathways, ecological networks, linguistic systems, and social systems—as well as man-made systems such as the World Wide Web and peer-to-peer networks. The contributed chapters in this volume are intended to promote cross-fertilization in several research areas, and will be valuable to newcomers in the field, experienced researchers, practitioners, and graduate students interested in systems exhibiting an underlying complex network structure in disciplines such as computer science, biology, statistical physics, nonlinear dynamics, linguistics, and the social sciences.

Geometric Theory of Dynamical Systems
Geometric Theory of Dynamical Systems

Author: J. Jr. Palis

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 208

ISBN-13: 1461257034

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... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

Evolutionary Dynamics of Complex Communications Networks
Evolutionary Dynamics of Complex Communications Networks

Author: Vasileios Karyotis

Publisher: CRC Press

Published: 2013-10-14

Total Pages: 297

ISBN-13: 1466518413

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Until recently, most network design techniques employed a bottom-up approach with lower protocol layer mechanisms affecting the development of higher ones. This approach, however, has not yielded fascinating results in the case of wireless distributed networks. Addressing the emerging aspects of modern network analysis and design, Evolutionary Dyna

Adaptive Networks
Adaptive Networks

Author: Thilo Gross

Publisher: Springer

Published: 2012-03-14

Total Pages: 332

ISBN-13: 9783642260148

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Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim “more is different”, is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word “network” one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of “more is different” appears in a different way in the present v- ume, from the viewpoint of what we call “adaptive networks.” Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

The Structure and Dynamics of Networks
The Structure and Dynamics of Networks

Author: Mark Newman

Publisher: Princeton University Press

Published: 2011-10-23

Total Pages: 593

ISBN-13: 1400841356

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From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society. But what exactly is a network? What different types of networks are there? Why are they interesting, and what can they tell us? In recent years, scientists from a range of fields--including mathematics, physics, computer science, sociology, and biology--have been pursuing these questions and building a new "science of networks." This book brings together for the first time a set of seminal articles representing research from across these disciplines. It is an ideal sourcebook for the key research in this fast-growing field. The book is organized into four sections, each preceded by an editors' introduction summarizing its contents and general theme. The first section sets the stage by discussing some of the historical antecedents of contemporary research in the area. From there the book moves to the empirical side of the science of networks before turning to the foundational modeling ideas that have been the focus of much subsequent activity. The book closes by taking the reader to the cutting edge of network science--the relationship between network structure and system dynamics. From network robustness to the spread of disease, this section offers a potpourri of topics on this rapidly expanding frontier of the new science.

Synchronization in Complex Networks of Nonlinear Dynamical Systems
Synchronization in Complex Networks of Nonlinear Dynamical Systems

Author: Chai Wah Wu

Publisher: World Scientific

Published: 2007

Total Pages: 168

ISBN-13: 9812709746

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This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.

Temporal Networks
Temporal Networks

Author: Petter Holme

Publisher: Springer

Published: 2013-05-23

Total Pages: 356

ISBN-13: 3642364616

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The concept of temporal networks is an extension of complex networks as a modeling framework to include information on when interactions between nodes happen. Many studies of the last decade examine how the static network structure affect dynamic systems on the network. In this traditional approach the temporal aspects are pre-encoded in the dynamic system model. Temporal-network methods, on the other hand, lift the temporal information from the level of system dynamics to the mathematical representation of the contact network itself. This framework becomes particularly useful for cases where there is a lot of structure and heterogeneity both in the timings of interaction events and the network topology. The advantage compared to common static network approaches is the ability to design more accurate models in order to explain and predict large-scale dynamic phenomena (such as, e.g., epidemic outbreaks and other spreading phenomena). On the other hand, temporal network methods are mathematically and conceptually more challenging. This book is intended as a first introduction and state-of-the art overview of this rapidly emerging field.

Fundamentals of Brain Network Analysis
Fundamentals of Brain Network Analysis

Author: Alex Fornito

Publisher: Academic Press

Published: 2016-03-04

Total Pages: 496

ISBN-13: 0124081185

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Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems - Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience - Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain