From complete disorder to near-perfect order: New research on complex systems in nature and engineering
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Scientists at the Center for Advancing Electronics Dresden (cfaed) demonstrate in a new study how systems can shift from disorder to near-perfect order with unprecedented abruptness. The research team of TUD Dresden University of Technology reveals with this study, published in Nature Communications, a novel class of transitions in coupled oscillatory units, termed "extreme synchronization transitions”, challenging our traditional understanding of phase transitions.
Phase transitions are fundamental phenomena emerging across natural and human-made systems – from ice melting and traffic jam formation to the magnetization of metals. They mark qualitative changes in the degree of ordering of system constituents. Understanding how and why these transitions emerge constitutes one of the cornerstones of research on complex systems in nature and engineering.
Traditionally, scientists have recognized two types of phase transitions:
- Continuous transitions, where order gradually increases after crossing a critical point (like a metal slowly becoming magnetic as temperature decreases)
- Discontinuous transitions, where order jumps from zero to an intermediate value at the critical point
"What makes our discovery remarkable is that in these extreme transitions, the system jumps directly from completely disordered to almost completely ordered at the critical point." explains Seungjae Lee, first author of the study. "This is fundamentally different from traditional phase transitions, in which the degree of order either changes gradually or jumps to intermediate levels at the critical point and only thereafter further slowly increases."
The study provides the first conceptual proof of such extreme transitions, exploiting mathematical properties of a natural (complex-variable) extension of the Kuramoto model, a paradigmatic model of coupled oscillators. The order formation here constitutes a synchronization process, a mutual adaptation of phases – the relative timing of the oscillatory units. Unlike conventional phase transitions that require infinite system sizes, these extreme transitions already occur in systems of just a few units and at relatively low coupling strengths. "While we understand the basic mechanisms in the model system we studied, determining the precise conditions for extreme transitions in other systems remains an open scientific challenge," noted Prof. Marc Timme, head of the Chair for Network Dynamics at TUD and last author of the study. "Previous studies as well as our own simulations suggest that related transitions may occur in various other systems, from chemical reactions to biological processes."
The implications of this research extend to multiple fields. In engineering applications, this knowledge could be crucial for power grid stability and swarm robotics coordination. "These findings not only advance our theoretical understanding of synchronization phenomena but also provide new tools for preventing or ensuring strong forms of synchrony in real-world systems," Timme added. The research opens new avenues for investigating similar phenomena in across systems, with potential applications ranging from disease treatment to technological innovation. Although contributing mechanisms in this study are principally understood, it is still not clear which mechanisms may co-act in which systems and which ingredients are required to realize or prevent extreme transitions.
Paper title: Extreme synchronization transitions
DOI: 10.1038/s41467-025-59729-8
Authors: Seungjae Lee, Lennart J. Kuklinski & Marc Timme
Published: Nature Communications, May 2025
Download: https://doi.org/10.1038/s41467-025-59729-8
Press image:
Image caption: Artistic illustration of a transition from disordered to ordered oscillation. (AI-generated)
Press inquiries:
TU Dresden, Center for Advancing Electronics Dresden:
Dr. Seungjae Lee, Chair of Network Dynamics
Tel.: +49 (0)351 463 43975
E-mail: seungjae.lee@tu-dresden.de
Prof. Marc Timme, Chair of Network Dynamics
Tel.: +49 (0)351 463 43972
E-mail: marc.timme@tu-dresden.de
Matthias Hahndorf
Science communication
Tel.: +49 (0)351 463 42847
E-mail: matthias.hahndorf@tu-dresden.de
About the Chair of Network Dynamics
The Chair of Network Dynamics headed by Prof. Marc Timme was established in 2017. The goal of this strategic professorship at TU Dresden, which is affiliated with both the research cluster "Center for Advancing Electronics Dresden" (cfaed) and the Institute for Theoretical Physics, is to bridge methods from applied mathematics and theoretical physics to applications in biology and engineering. It is the first professorship for network dynamics in this cross-disciplinary character in Central Europe. Since networks are almost everywhere around us, the research team aims to unify understanding of the fundamental mechanisms underlying the collective dynamics of large, nonlinear, interconnected systems by combining fundamental theoretical descriptions with data-driven analysis and modeling. An essential part of their work in investigating self-organized systemic effects and developing new conceptual perspectives for theoretical as well as computational tools necessary to understand these dynamics. This understanding is the basis for predicting and ultimately controlling the behavior of complex networked systems.
Further information: http://networkdynamics.info
About cfaed - Center for Advancing Electronics Dresden
The cfaed is a research cluster at TUD Dresden University of Technology. As an interdisciplinary research center for perspectives in electronics, it is located at the TUD as a central scientific institution and integrates members from non-university research institutions in Saxony and Saxony-Anhalt as well as the TU Chemnitz. The cluster is dedicated to the fundamentals of future-proof information technologies that would not be possible with today's silicon-based devices. To achieve its goals, the cfaed combines the thirst for knowledge of the natural sciences with the innovative power of the engineering sciences.