Abstract
Order parameters have proved a vital tool for simplifying and understanding complex dynamics in a range of physical systems. However, applying these approaches to the high-dimensional time-dependent variability inherent to thermodynamically open systems—such as those found in neural networks and climate dynamics—remains a challenge. We introduce a novel order parameter based on alignment of component frequencies, in contrast to the widely used Kuramoto order parameter’s alignment of process phases. We present numerical simulations comparing this new parameter to the Kuramoto order parameter in a range of models, including a prototypical phase-oscillator model relevant to many open systems, such as neuronal dynamics. These results show that the new parameter more accurately identifies synchronisation in conditions characteristic of open systems, revealing dynamics entirely missed by established methods.
| Original language | English |
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| Number of pages | 13 |
| Journal | European Physical Journal: Special Topics |
| Early online date | 3 Nov 2025 |
| DOIs | |
| Publication status | E-pub ahead of print - 3 Nov 2025 |
Bibliographical note
Copyright © The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.Funding
The work was supported by the Sony Research Award Program, the Engineering and Physical Sciences Research Council, UK (Grant No. EP/X004597/1 and MAA7977 Mathematical Sciences Research Associates grant EP/W522612/1), the EU’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 642563, and Aston Digital Futures Institute.