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Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences. Copyright © 2020 Elsevier B.V. or its licensors or contributors. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. We also take an overview of the new emergent features coming out from the interplay between the structure and the function of the underlying patterns of connections. 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. System Upgrade on Fri, Jun 26th, 2020 at 5pm (ET) During this period, our website will be offline for less than an hour but the E-commerce and registration of new users may not be available for up to 4 hours. © 2020 World Scientific Publishing Co Pte Ltd, Nonlinear Science, Chaos & Dynamical Systems, Graphs, Networks, Laplacian Matrices and Algebraic Connectivity, 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, Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems, Synchronization in Networks of Coupled Discrete-Time Systems, Erdös number and scientific collaboration network, Algebraic connectivity of small-world networks, Algebraic connectivity and degree sequence, Synchronization and algebraic connectivity, Coupling topology with a spanning directed tree, Synchronization criteria based on algebraic connectivity, Synchronization of coupled scalar maps via contractivity of operators, Nonautonomous coupling: continuous-time case, Nonautonomous coupling: discrete-time case, Ergodicity of inhomogeneous Markov chains, Pseudocontractivity and scrambling stochastic matrices, Set-nonexpansive and set-contractive operators, Set-contractivity under the Euclidean norm, Set-contractivity under a weighted Euclidean norm, Set-contractivity and coefficient of ergodicity, Follow the leader dynamics and leadership in coordinated agents, Synchronization in random networks without the scrambling condition, Appendix A Algebraic Connectivity and Combinatorial Properties of a Graph. By continuing to browse the site, you consent to the use of our cookies. Chapter 1: Introduction (76k). The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. Extensive numerical work as well as analytical approaches to the problem are presented. We use cookies to help provide and enhance our service and tailor content and ads. By continuing you agree to the use of cookies. Florian Dörflera,b,1, Michael Chertkovb, and Francesco Bulloa. Synchronization processes in populations of locally interacting elements are the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understanding synchronization phenomena in natural systems now take advantage of the recent theory of complex networks. Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. Synchronization processes in populations of locally interacting elements are the focus of intense research in physical, biological, chemical, technological and social systems. By continuing you agree to the use of cookies. Moreover, the coupled oscillator model (1)serves as the prototypical example for synchronization in complex networks (Arenas et al., 2008, Boccaletti et al., 2006, Osipov et al., 2007, Strogatz, 2001, Suykens and Osipov, 2008), and its linearization is the well-known consensus protocol studied in networked control; see the surveys and monographs (Bullo et al., 2009, Garin and Schenato, … Synchronization processes in populations of locally interacting elements are the focus of intense research in physical, biological, chemical, technological and social systems. Abstract. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Title:Synchronization in complex networks. This paper attempts to present an overview of recent progress of synchronization of complex dynamical networks and its applications. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. Synchronization in complex oscillator networks and smart grids.

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