Swarmalators: The fusion of sync and swarm

Swarmalator systems intertwine two forms of collective behavior—swarming and synchronization—leading to the emergence of space-time patterns. Our research advances both the foundations and application of swarmalators, with emphasis on the real-world challenges of deploying this concept in robots and drones.

Swarming and synchronization are two fascinating manifestations of collective behavior in nature. Swarming means that many entities act together as a coordinated group, like in bird flocks, fish schools, and insect swarms. Synchronization means that entities coordinate their internal rhythms in time, like in the synchronous flashing of fireflies or the collective beating of cardiac cells. Traditionally, these two phenomena have been studied as being independent from each other. But what would happen if we considered a joint model for swarming and synchronization? What if we coupled them in such a way that movement depends on synchrony and synchrony depends on movement?

Keynote at ACSOS 2024

Keynote at IEEE ACSOS in Aarhus. Photo by L. Esterle.

This is exactly what swarmalators do. Each swarmalator adjusts its clock based on the clock values and positions of other swarmalators. And it performs movements based on both the positions and clock values of other swarmalators. The term swarmalator was introduced by O’Keeffe, Hong, and Strogatz in 2017, igniting a new line of research.

The concept is not just a theoretical construct but is relevant in the real world, like in microswimmers and magnetism, and holds great promise for applications in mobile robotics, where coordinated motion and timing are essential for adaptive and scalable behavior.

Research at Klagenfurt

Bettstetter and his team, together with collaborators, aim to advance both the theory and application of swarmalators by adapting the mathematical model for real robots and drones—addressing real-world challenges such as communication and movement constraints. The University of Klagenfurt was among the first, if not the first, to implement swarmalators in a physical robotic system and demonstrate swarmalators experimentally.

Their research directions include the following:

  • Analyze and characterize emergent patterns in swarmalator systems
  • Propose and assess extensions to the swarmalator model for practical applications
  • Adapt and implement the swarmalator concept in mobile robotics including drones

Specifically, Bettstetter develops swarmalator systems that perform time-discrete coupling and local interactions, as required for technical applications, rather than the continuous, globally interactions assumed in the original model. A complementary line of research exploits the concept of randomized coupling in swarmalator systems to account for unreliable interactions or to reduce communication overhead.

Publications

Talks

Software

Tutorial: What are swarmalators and their basic patterns?

This video by Christian Bettstetter explains the concept of swarmalators, discusses the five basic emergent patterns, and outlines applications in nature and technology (2024).

Podcast

This Podcast-style dialog introduces swarmalators and discusses the five basic patterns. It was created by Google’s NotebookLM based on the above video.

Robotic swarmalators

This video shows our multi-robot system that forms emergent space-time patterns inspired by the theory of swarmalators, core part of the doctoral thesis of Agata Barcis as part of a Popper school (2020).


This work highlights a multi-drone system that performs a swarmalator system implemented on Crazyflies using the Crazyswarm platform (2019).


This work realizes and studies, for the first time, the concept of swarmalators in robotic systems (2018)

. . .