Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 8: Nonlinear Dynamics, Synchronization, and Chaos
DY 8.3: Vortrag
Montag, 9. März 2026, 10:00–10:15, ZEU/0118
From quaternion order parameter to extreme synchronization transitions — •Moritz Thümler1, Seungjae Lee1, Lennart J. Kuklinski1, and Marc Timme1,2 — 1Chair of Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany — 2Lakeside Labs, Lakeside B04b , 9020 Klagenfurt, Austria
Synchrony plays a fundamental role in the operation of many systems across physics, biology, and engineering. Fifty years after the introduction of the paradigmatic Kuramoto model*which provides a mathematically tractable framework for studying transitions to synchrony*several open questions remain, particularly concerning finite-size systems. An analytic continuation of the Kuramoto model from real to complex variables has been proposed to address this challenge [1]. Here, we introduce a generalized quaternion order parameter that captures complex-valued state vectors and demonstrate its effectiveness by uncovering a link between real-valued Kuramoto dynamics and complex locked states calculated via self-consistency and newly uncovered explosive transitions to synchrony [2].
[1]*Moritz Thümler et al., Synchrony for Weak Coupling in the Complexified Kuramoto Model, Physical Review Letters 130:187201 (2023).
[2] Lee, Seungjae, Kuklinski, Lennart J., Thümler, Moritz and Timme, Marc. "Hopf-induced desynchronization" Zeitschrift für Naturforschung A, vol. 80, no. 11, 2025,
Keywords: Analytic continuation; Kuramoto model; Synchronization