Synchronization in complex networks

By Alex Arenas, Albert Díaz-Guilera, Jürgen Kurths, Yamir Moreno, Changsong Zhou. 2008

3,485 citations recorded by the source corpus.

Synchronization in complex networks Alex Arenas, 1, 2, 3 Albert D´ iaz-Guilera, 4, 2 Jurgen Kurths, 5 Yamir Moreno, 2, 6 and Changsong Zhou 7 Departament d’Enginyeria Inform` tica i Matem` tiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain a a Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Departament de F´ isica Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain Institute of Physics, University of Potsdam PF 601553, 14415 Potsdam, Germany Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (Dated: February 6, 2008) Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many eﬀorts de- voted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. 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. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive nu- merical work as well as analytical approaches to the problem are presented. 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. PACS numbers: 05.45.Xt,89.75.Fb,89.75.Hc Contents I. Introduction II. Complex networks in a nutshell III. Coupled phase oscillator models on complex networks A. Phase oscillators 1. The Kuramoto model 2. Kuramoto model on complex networks 3. Onset of synchronization in complex networks 4. Path towards synchronization in complex networks 5. Kuramoto model on structured or modular networks 6. Synchronization by pacemakers B. Pulse-coupled models C. Coupled maps IV. Stability of the synchronized state in complex networks A. Master Stability Function formalism 1. Linear Stability and Master Stability Function 2. Measures of synchronizability 3. Synchronizability of typical network models 4. Synchronizability and structural characteristics of networks 5. Graph theoretical bounds to synchronizability 6. Synchronizability of weighted networks 7. Universal parameters controlling the synchronizability B. Design of synchronizable networks 1. Weighted couplings for enhancing synchronizability 2. Topological modiﬁcation for enhancing synchronizability 3. Optimization of synchronizability C. Beyond the Master Stability Function formalism V. Applications A. Biological systems and neuroscience 1. Genetic networks 2. Circadian rhythms 3. Ecology 4. Neuronal networks 5. Cortical networks B. Computer science and engineering 1. Parallel/Distributed computation 2. Data mining 3. Consensus problems 4. Communication networks 5. Material and traﬃc ﬂow 6. Power-grids C. Social sciences and economy 1. Opinion formation 2. Finance 3. World Trade Web D. Perspectives VI. Conclusions Acknowledgments References I. INTRODUCTION Synchronization, as an emerging phenomenon of a pop- ulation of dynamically interacting units, has fascinated humans from ancestral times. No matter whether the phenomenon is spontaneous or induced, synchronization captivates our minds and becomes one of the most in- teresting scientiﬁc problems. Synchronization processes are ubiquitous in nature and play a very important role in many diﬀerent contexts as biology, ecology, climatol- ogy, sociology, technology, or even in arts ((Osipov et al., 2007; Pikovsky et al., 2001). It is known that synchrony

Subfields: Cognitive Neuroscience, Computer Networks and Communications

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Citations in the corpus

Coupling functions:universal insights into dynamical interaction mechanisms (2017, background): “…1976), breathers (MacKay and Aubry, 1994), coexisting phases (Keller et al., 1992), fractal dimensions (Aguirre et al., 2009), network dynamics (Arenas et al., 2008; Boccaletti et al., 2006), and coupling strength and directionality (Hlaváčkováá-Schindler et al., 2007; Marwan et al.,…”
Missing and spurious interactions and the reconstruction of complex networks (2009, background): “…in the network [31]; E , Synchronizability, that is, the ratio between the largest eigenvalue and the smallest non-zero eigenvalue of the Laplacian matrix of the network [32]; F , Spreading threshold, that is, the ratio between the ﬁrst and the second moments of the degree distribution [33].”
Mathematical Formulation of Multilayer Networks (2013, methodology): “As an example, let’s consider the most intuitive weighting procedure: for each pair of layers (h̃k̃), we sum all of the weights in the connections between their nodes to obtain edge weights of qh̃k̃ = C α β (h̃k̃)U β α .”
Synchronization via Pinning Control on General Complex Networks (2013, background): “[1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61] and consensus [6, 51, 52, 53, 55, 59, 64] in very large-scale complex networks.”
The structure and dynamics of multilayer networks (2014, background): “[10,11] constitute important accounts on the state of the art for what concerns the study of synchronous organization of networking systems [11], and processes like evolutionary games on networks [10].”
Control Principles of Complex Networks (2015, methodology): “In particular the study of network-mediated synchronization has a long history, with applications from biology to neuroscience, engineering, computer science, economy and social sciences (Arenas et al., 2008).”
Recurrence-based time series analysis by means of complex network methods (2010, methodology): “For a more detailed overview, we refer to [Marwan et al. , 2007b; Bandt et al. , 2008].”
Generalized synchronization between two different complex networks (2012, background): “Till now there have been a huge number of publications [3].”
Cluster synchronization in nonlinear complex networks under sliding mode control (2016, background): “Synchronization processes are ubiquitous in nature and play a very important role in many different aspects such as biology, ecology, climatology, sociology, and technology [9–15].”