From complete disorder to near-perfect order: New research on complex systems in nature and engineering

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 information:

Title: Extreme synchronization transitions
Authors: Seungjae Lee, Lennart J. Kuklinski & Marc Timme
DOI: 10.1038/s41467-025-59729-8
Published: Nature Communications, May 2025
Download: https://doi.org/10.1038/s41467-025-59729-8

Contact:

Center for Advancing Electronics Dresden:

Dr. Seungjae Lee
Chair of Network Dynamics
Tel.: +49 (0)351 463 43975
Email:

Prof. Marc Timme
Chair of Network Dynamics
Tel.: +49 (0)351 463 43972
Email:

Matthias Hahndorf
Science communication
Tel.: +49 (0)351 463 42847
Email: