Emergence of structural patterns out of synchronization in networks with competitive interactions

Assenza, Salvatore; Gutiérrez, Ricardo; Gómez‐Gardeñes, Jesús; Latora, Vito; Boccaletti, Stefano

doi:10.1038/srep00099

Cited by 88 publications

(74 citation statements)

References 53 publications

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“…Following the same simulation process, the time evolution of r can exhibit quasi-periodic oscillations for some special coupling strengths [222]. Interestingly, the network dynamics with competitive interactions (Eqs.…”

Section: Time-varying Couplingmentioning

confidence: 99%

“…In directed networks with the same incoming and outgoing links, the coupling weights w ij can also bes adjusted as [222] …”

Section: Time-varying Couplingmentioning

confidence: 99%

“…Coupling w ij is the non-negative and time-dependent weight of a directed link from node j to i in [221,222]. The adaptive evolution of the weights w ij is defined as follows [221]ẇ…”

Section: Time-varying Couplingmentioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: Time-varying Couplingmentioning

confidence: 99%

“…In directed networks with the same incoming and outgoing links, the coupling weights w ij can also bes adjusted as [222] …”

Section: Time-varying Couplingmentioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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“…In this work, we approach the problem of delaying jammed states from the perspective of adaptive networks [26], which has been successfully used as a way for enhancing the functionality of network topologies in diverse settings such as synchronization [27][28][29][30][31], sustainability of cooperation in evolutionary games [33], or resilience to epidemics [32]. In our case, the network topology of the communication system will adapt its connections in order to avoid congestion.…”

Section: Introductionmentioning

confidence: 99%

Reciprocal interactions out of congestion-free adaptive networks

2012

Self Cite

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In this paper we study the jamming transition in complex adaptive networks. We introduce an adaptation mechanism that modifies the weight of the communication channels in order to delay the congestion onset. Adaptivity takes place locally as it is driven by each node of the network. Surprisingly, regardless of the structural properties of the backbone topology, e.g., its degree distribution, the adaptive network can reach optimal functioning provided it allows a reciprocal distribution of the weights. Under this condition, the optimal functioning is achieved through an extensive network reshaping ending up in a highly reciprocal weighted network whose critical onset of congestion is delayed up to its maximum possible value. We also show that, for a given network, the reciprocal weighting obtained from adaptation produce optimal static configurations.

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“…Most works that employ coevolutionary dynamics have focused on the characterization of the phenomenon of network fragmentation arising from this competition. Although community structures have been found in some coevolutionary systems [30][31][32][33], investigating the mechanisms for the formation of perdurable communities remains an open problem.…”

Section: Introductionmentioning

confidence: 99%

Emergence and persistence of communities in coevolutionary networks

González-Avella¹,

Cosenza²,

Herrera³

et al. 2014

EPL

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We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an adaptive rewiring process and a node dynamics given by a simple voterlike rule. We find that, for some values of the parameters describing the adaptive rewiring process, a community structure emerges on a connected network. We show that the emergence of communities is associated to a decrease in the number of active links in the system, i.e. links that connect two nodes in different states. The lifetime of the community structure state scales exponentially with the size of the system. Additionally, we find that a small noise in the node dynamics can sustain a diversity of states and a community structure in time in a finite size system. Thus, large system size and/or local noise can explain the persistence of communities and diversity in many real systems.

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Emergence of structural patterns out of synchronization in networks with competitive interactions

Cited by 88 publications

References 53 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Reciprocal interactions out of congestion-free adaptive networks

Emergence and persistence of communities in coevolutionary networks

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