Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

I. Video Conference [16:15]

Prof. Francisco A. Rodrigues (University of São Paulo, Project C11)

Title: Explosive synchronization in complex networks

Synchronization is a ubiquitous phenomenon in both the natural world and in technology. Kuramoto oscillators display a second-order phase transition to the synchronous state with a critical coupling strength that depends on the network topology. Recently, it has been observed that a first-ordersynchronization transition can be observed in complex networks when there is a positive correlation between the heterogeneity of the connections and the natural frequencies of the oscillators. This phenomenon is called explosive synchronization. In this presentation, we consider mean-field approximations to determine the critical coupling of explosive synchronization in complex networks. We demonstrate that the equation obtained for the critical coupling has an inverse dependence on the network average degree. Moreover, we show that the inclusion of time-delay enhances the level ofsynchronization. Finally, we demonstrate that the nodes in a second-order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

References:

Peng Ji, Thomas K.D. M. Peron, Peter J. Menck, Francisco A. Rodrigues and Jürgen Kurths, Cluster Explosive Synchronization in complex networks, Physical Review Letters, 110, 218701 (2013).

Thomas K. D. M. Peron and Francisco A. Rodrigues, Determining the critical coupling of explosivesynchronization transitions in scale-free networks by mean-field approximations, Physical Review E, vol. 86, issue 5, 056108, (2012).

Thomas K. D. M. Peron and Francisco A. Rodrigues, Explosive synchronization enhanced by time-delayed coupling, Physical Review E, vol. 86, issue 1, 016102 (2012).

II. Meeting of Members (All PIs and PhDs) [approx. 17:30]

1. Bericht über Treffen der IRTGs in Berlin

2. Entwicklung und Zukunft
- Fortsetzungsantrag, Zeitplan, PIs
- Inhaltliche Ausrichtung
- Fortsetzungsprojekte

3. Nächste Generation von PhDs
- Übersicht / Zeitplan
- DFG-Anschubförderung
- Ausschreiben & Einstellen

4. Konferenz und Schule in Brasilien
- Übersicht
- Exkursion
- Flüge

5. Weiteres