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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 Thümler¹, Shesha G.M. Sriniva², Malte Schröder¹, and Marc Timme^1,3 — ¹Chair for Network Dynamics, Institute of Theoretical Physics & Center for Advancing Electronics Dresden (cfaed), TU Dresden — ²Institute of Physics and Material Sciences, Universite du Luxembourg — ³Lakeside 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.