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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Explosive synchronization is discontinuous

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Vlasov, Vladimir [1] ; Zou, Yong [2] ; Pereira, Tiago [3, 4]
Total Authors: 3
[1] Univ Potsdam, Inst Phys, D-14469 Potsdam - Germany
[2] E China Normal Univ, Dept Phys, Shanghai 200062 - Peoples R China
[3] Univ Sao Paulo, Inst Math & Comp Sci, Sao Paulo - Brazil
[4] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ - England
Total Affiliations: 4
Document type: Journal article
Source: Physical Review E; v. 92, n. 1 JUL 6 2015.
Web of Science Citations: 16

Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated with the node degree. This explosive transition was conjectured to be discontinuous. Indeed, numerical investigations reveal a hysteresis behavior associated with the transition. Here, we analyze explosive synchronization in star graphs. We show that in the thermodynamic limit the transition to (and out of) collective behavior is indeed discontinuous. The discontinuous nature of the transition is related to the nonlinear behavior of the order parameter, which in the thermodynamic limit exhibits multiple fixed points. Moreover, we unravel the hysteresis behavior in terms of the graph parameters. Our numerical results show that finite-size graphs are well described by our predictions. (AU)

FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants