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Synchronization of Kuramoto Oscillators in Complex Networks

Grant number: 12/22160-7
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2013
Effective date (End): July 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal researcher:Francisco Aparecido Rodrigues
Grantee:Thomas Kaue Dal Maso Peron
Home Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated scholarship(s):15/02486-3 - Synchronization of Kuramoto oscillators in complex networks, BE.EP.DR


Several kinds of complex systems can be described in terms of complex networks, for instance, electrical power grids, metabolic networks, Internet and social networks. The mathematical concept of network has recently been turned into an important tool for describing complex systems, whose principal characteristic is that they consist of a large number of mutually interacting dynamical parts which are coupled in a nonlinear fashion. The theory of complex networks attempts to explain the structure of interactions between the subunits of a system in order to understand their functioning and the processes taking place in them. It tries, for instance, to grasp how the structure of social networks affects the spread of information or human diseases or even how the structure of the World Wide Web influences the search engines and surfing behavior. In this project, we will study how the topology influences the emergence of collective behavior in a population of oscillators. More specifically, we will study synchronization processes in networks in which the local topology presents cycles of order three and arbitrary distributions of subgraphs. Moreover, in order to investigate synchronization processes in systems with characteristics more similar to those observed in real systems, we will extend the models in order to include assortativity, noise and delays in the connections. These studies will allow a better comprehension about synchronization in real networks, once the models reported in the literature are based on results derived for the traditional configuration model in the absence of fluctuations and perturbations, which fails to describe the local topology and, consequently, the dynamics of real-world networks.

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Scientific publications (11)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
YE, CHENG; COMIN, CESAR H.; PERON, THOMAS K. D. M.; SILVA, FILIPI N.; RODRIGUES, FRANCISCO A.; COSTA, LUCIANO DA F.; TORSELLO, ANDREA; HANCOCK, EDWIN R.. Thermodynamic characterization of networks using graph polynomials. Physical Review E, v. 92, n. 3, . (12/50986-7, 12/22160-7, 11/50761-2, 11/22639-8, 13/26416-9)
SONNENSCHEIN, BERNARD; PERON, THOMAS K. D. M.; RODRIGUES, FRANCISCO A.; KURTHS, JUERGEN; SCHIMANSKY-GEIER, LUTZ. Collective dynamics in two populations of noisy oscillators with asymmetric interactions. Physical Review E, v. 91, n. 6, . (13/26416-9, 12/22160-7)
RODRIGUES, FRANCISCO A.; PERON, THOMAS K. D. M.; JI, PENG; KURTHS, JUERGEN. The Kuramoto model in complex networks. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, v. 610, p. 1-98, . (12/22160-7, 13/26416-9, 15/02486-3)
EROGLU, DENIZ; PERON, THOMAS K. D. M.; MARWAN, NOBERT; RODRIGUES, FRANCISCO A.; COSTA, LUCIANO DA F.; SEBEK, MICHAEL; KISS, ISTVAN Z.; KURTHS, JUERGEN. Entropy of weighted recurrence plots. Physical Review E, v. 90, n. 4, . (11/50761-2, 13/26416-9, 12/22160-7)
PERON, THOMAS K. DM.; KURTHS, JUERGEN; RODRIGUES, FRANCISCO A.; SCHIMANSKY-GEIER, LUTZ; SONNENSCHEIN, BERNARD. Traveling phase waves in asymmetric networks of noisy chaotic attractors. Physical Review E, v. 94, n. 4, . (13/26416-9, 15/02486-3, 12/22160-7)
PERON, T. K. D.; COMIN, C. H.; AMANCIO, D. R.; COSTA, L. DA F.; RODRIGUES, F. A.; KURTHS, J.. Correlations between climate network and relief data. Nonlinear Processes in Geophysics, v. 21, n. 6, p. 1127-1132, . (13/06717-4, 11/22639-8, 12/22160-7, 10/19440-2)
SCHULTZ, PAUL; PERON, THOMAS; EROGLU, DENIZ; STEMLER, THOMAS; AVILA, GONZALO MARCELO RAMIREZ; RODRIGUES, FRANCISCO A.; KURTHS, JURGEN. Tweaking synchronization by connectivity modifications. Physical Review E, v. 93, n. 6, . (12/22160-7, 15/02486-3)
SILVA, FILIPI N.; COMIN, CESAR H.; PERON, THOMAS K. D. M.; RODRIGUES, FRANCISCO A.; YE, CHENG; WILSON, RICHARD C.; HANCOCK, EDWIN R.; COSTA, LUCIANO DA F.. Concentric network symmetry. INFORMATION SCIENCES, v. 333, p. 61-80, . (12/50986-7, 12/22160-7, 11/50761-2, 11/22639-8, 13/26416-9)
JI, PENG; PERON, THOMAS K. D. M.; RODRIGUES, FRANCISCO A.; KURTHS, JUEURGEN. Analysis of cluster explosive synchronization in complex networks. Physical Review E, v. 90, n. 6, . (11/50761-2, 13/26416-9, 12/22160-7)
MENDEZ-BERMUDEZ, J. A.; ALCAZAR-LOPEZ, A.; MARTINEZ-MENDOZA, A. J.; RODRIGUES, FRANCISCO A.; PERON, THOMAS K. D. M.. Universality in the spectral and eigenfunction properties of random networks. Physical Review E, v. 91, n. 3, . (11/50761-2, 13/26416-9, 12/22160-7)
SONNENSCHEIN, BERNARD; PERON, THOMAS K. D. M.; RODRIGUES, FRANCISCO A.; KURTHS, JUERGEN; SCHIMANSKY-GEIER, LUTZ. Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations. European Physical Journal B, v. 87, n. 8, . (13/26416-9, 12/22160-7)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
PERON, Thomas Kaue Dal Maso. Dynamics of Kuramoto oscillators in complex networks. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT) São Carlos.

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