# SKM 2023 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# DY: Fachverband Dynamik und Statistische Physik

## DY 18: Nonlinear Dynamics, Synchronization and Chaos

### DY 18.1: Vortrag

### Dienstag, 28. März 2023, 10:00–10:15, ZEU 148

Synchrony at Weak Coupling in the Complexified Kuramoto Model — •Moritz Thümler^{1}, Shesha G.M. Sriniva^{2}, Malte Schröder^{1}, and Marc Timme^{1,3} — ^{1}Chair for Network Dynamics, Institute of Theoretical Physics & Center for Advancing Electronics Dresden (cfaed), TU Dresden — ^{2}Institute of Physics and Material Sciences, Universite du Luxembourg — ^{3}Lakeside Labs, Klagenfurt, Austria

We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics.
For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system.
However, synchrony persists in the form of complex locked states
for coupling strengths K below the transition K^{(pl)} to classical phase locking.
Where complex locked states are stable, their imaginary parts indicate which units belong to the locked population in the original, real-variable system. We uncover a second transition at K′<K^{(pl)} below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.
The results open up a path towards a new field of network dynamics with variables complexified by analytic continuation.