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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.)

SYNCHRONIZATION IN NETWORKS WITH STRONGLY DELAYED COUPLINGS

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Author(s):
Maia, Daniel M. N. [1, 2] ; Macau, Elbert E. N. [1] ; Pereira, Tiago [3] ; Yanchuk, Serhiy [4]
Total Authors: 4
Affiliation:
[1] Natl Inst Space Res INPE, Associate Lab Appl Comp & Math LAC, Av Astronautas 1758, BR-12227010 Sao Jose Dos Campos, SP - Brazil
[2] State Univ Rio Grande do Norte UERN, Dept Math & Stat, BR-59610210 Mossoro, RN - Brazil
[3] Univ Sao Paulo, Inst Math & Comp Sci ICMC, Av Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil
[4] Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin - Germany
Total Affiliations: 4
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 23, n. 8, p. 3461-3482, OCT 2018.
Web of Science Citations: 0
Abstract

We investigate the stability of synchronization in networks of dynamical systems with strongly delayed connections. We obtain strict conditions for synchronization of periodic and equilibrium solutions. In particular, we show the existence of a critical coupling strength kappa(c), depending only on the network structure, isolated dynamics and coupling function, such that for large delay and coupling strength kappa < kappa(c) the network possesses stable synchronization. The critical coupling kappa(c) can be chosen independently of the delay for the case of equilibria, while for the periodic solution, kappa(c) depends essentially on the delay and vanishes as the delay increases. We observe that, for random networks, the synchronization interval is maximal when the network is close to the connectivity threshold. We also derive scaling of the coupling parameter that allows for a synchronization of large networks for different network topologies. (AU)

FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants