Network synchronization: Spectral versus statistical properties

Atay, Fatihcan M.; Bıyıkoğlu, Türker; Jost, Jürgen

doi:10.1016/j.physd.2006.09.018

Cited by 94 publications

(93 citation statements)

References 36 publications

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“…Moreover, in the system of coupled oscillators which we consider below, superior synchronization is essentially related to maximizing the second smallest eigenvalue of the graph Laplacian. This eigenvalue -the algebraic connectivity-is an important invariant for undirected graphs and is, e.g., relevant for the analysis of the robustness of networks against node removal or for epidemic spreading [3]. …”

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confidence: 99%

Small worlds in space: Synchronization, spatial and relational modularity

Brede¹

2010

EPL

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Abstract. -In this Letter we investigate networks that have been optimized to realize a trade-off between enhanced synchronization and cost of wire to connect the nodes in space. Analyzing the evolved arrangement of nodes in space and their corresponding network topology a class of small world networks characterized by spatial and network modularity is found. More precisely, for low cost of wire optimal configurations are characterized by a division of nodes into two spatial groups with maximum distance from each other, whereas network modularity is low. For high cost of wire, the nodes organize into several distinct groups in space that correspond to network modules connected on a ring. In between, spatially and relationally modular small world networks are found.Introduction. -Synchronization phenomena occur in a diverse range of contexts in nature, engineering and society: cardiac pacemaker cells, neurons in the brain, fireflies that flash in unison, the power grid or consensus formation among people are just a few example applications from these fields. All of these are distributed systems embedded in space in which most couplings are local, but often also non-local long range couplings are present. Hence, most of these systems can be described as small world (SW) networks [1]: nodes represent elementary units of the system such as neurons, fireflies, power stations or people and links in the network represent interactions that describe how the elementary units influence each other. Synchronization phenomena on SW and other complex networks have found much attention in the recent literature, see, e.g. [2], for a review. Moreover, in the system of coupled oscillators which we consider below, superior synchronization is essentially related to maximizing the second smallest eigenvalue of the graph Laplacian. This eigenvalue -the algebraic connectivity-is an important invariant for undirected graphs and is, e.g., relevant for the analysis of the robustness of networks against node removal or for epidemic spreading [3].

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confidence: 99%

Small worlds in space: Synchronization, spatial and relational modularity

Brede¹

2010

EPL

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“…This set can be sorted as . Normalizing L using the corresponding eigenvectors , , results in (18) At this stage, a small perturbation of the state is dictated by the equation [26], [27]. Along the eigenvector of (18), the perturbation is given by (19) One solution for (19) is [27] (20)…”

Section: Theoretical Analysismentioning

confidence: 99%

Impact of Topological Characteristics on Consensus Building in Multiagent Systems

Hatime

2011

IEEE Sensors J.

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Abstract-This paper represents a network of nodes as a graph and investigates the impact of topological characteristics on consensus building. The properties evaluated are the algebraic connectivity ratio, average path, average cluster coefficient, average matching index, modularity, and the average participation. The consensus is measured by the average number of state updates that the system requires to get the global scope of the task at hand. Factor analysis and regression analysis are applied to analyze the impact of the topological characteristics, to understand the dependencies among them and to reduce the dimensionality of the analysis. A theoretical study is provided to support the results obtained by the statistical method. The insights from the analysis are discussed.

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“…Various studies have attempted to link network characteristics such as clustering [9,10,11,12], degree mixing [9,13], pathlength [14,15] or betweenness centrality [15,16,10] to the PFS. More detailed analyses, however, show that such a characterization is at most meaningful in a statistical sense, since synchronization appears to be determined by 'fine' details of the organization of the coupling network [17]. Thus, linking synchronization properties to statistical network measures often provides only a rule of thumb.…”

Section: Introductionmentioning

confidence: 99%

Optimal synchronization on strongly connected directed networks

Brede

2010

Eur. Phys. J. B

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Abstract. In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the particular organization of the core and the periphery-core linkage. PACS

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Network synchronization: Spectral versus statistical properties

Cited by 94 publications

References 36 publications

Small worlds in space: Synchronization, spatial and relational modularity

Small worlds in space: Synchronization, spatial and relational modularity

Impact of Topological Characteristics on Consensus Building in Multiagent Systems

Optimal synchronization on strongly connected directed networks

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