Emerging math from emergent synchrony

The National Science Foundation Division of Mathematical Sciences awarded Northwestern University $299,976 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate collective synchronization in biological systems.

The project examines how individuals in a group achieve synchronized action without a central leader or orchestrator, focusing on two real-world cases: synchronous flashing in firefly swarms and coordinated waving in fiddler crab groups. The research team will generate large-scale spatio-temporal datasets using drone-based and stereo videography in field environments, design and deploy novel experiments to test synchronization mechanisms, and develop mathematical models that reveal universal principles of collective behavior across species. The work addresses temporal self-organization in biological systems—specifically how animals synchronize without an apparent external timing cue—and explores how interventions can maintain or disrupt synchronization, with potential applications to engineered systems such as power grids where loss of synchronization triggers cascading failures. The project also incorporates public engagement through collaboration with artists to produce multimedia storytelling and visual art projects for schools, communities, and general audiences.

Work is performed at Northwestern University's Evanston, Illinois campus. The period of performance runs from September 1, 2026, through August 31, 2029. This is a project grant, the standard assistance type for investigator-initiated research under NSF's Mathematical and Physical Sciences program.

Abstract

How can individuals in a group all act in unison, without any leader or orchestrator that guides them? This project investigates this phenomenon, seen throughout nature. The research team will study two real-world examples: synchronous flashing firefly swarms and groups of waving fiddler crabs. By combining large-scale measurements, novel field experiments, and mathematical modeling, the project aims to reveal fundamental principles of how and why collective synchronization emerges. Because these two animal groups are very different, comparing them may uncover universal rules of nature as well as critical differences between species. Beyond advancing basic science, this research addresses the global crisis of declining insect populations and biodiversity loss by determining how to protect these fragile ecological systems. Furthermore, the team will use mathematical models and experiments to explore how interventions can maintain or disrupt synchronization. This understanding is vital for engineered systems that depend heavily on precise timing, such as the US power grid, where a loss of synchronization can trigger widespread blackouts. Finally, the project aims to bring science to the public. The team is collaborating with artists to produce multimedia projects, including storytelling and visual arts, to share their scientific discoveries with schools, communities, and the general public. This research addresses fundamental problems in temporal self-organization, specifically how biological systems can synchronize with no apparent zeitgeber. To bridge the GAP between theoretical models and experimental data, the project focuses on two distinct animal groups whose relatively stationary positions during signaling make their collective behavior highly tractable. The research objectives are to: (i) generate large-scale spatio-temporal datasets using drone-based and stereo videography in novel field environments; (II) design and deploy experimental apparatuses that enable open- and closed-loop interactions with wild populations; and (III) pose and test new coupled oscillator models of relevance to the biology - offering a promising foundation for new mathematics. Comparing two distinct species allows the investigators to isolate general underlying mechanisms of collective behavior from species-specific constraints, establishing a methodological framework for future comparative studies. Outcomes should be of interest to a wide range of researchers, ranging from applied mathematicians focused on nonlinear dynamics or network/complexity science to evolutionary biologists and ecologists. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.