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Oscillators that sync and swarm, specifically oscillators whose phase and spatial dynamics are coupled together.

Proposed potential swarmalators include groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact. An additional example of a possible swarmalator system, is a population of myxobacteria, modeled by Igoshin and colleagues in 2001.

The study of swarmalators brings together the physics and biology of swarms and synchronization. Swarm studies focus on the movement of animals while neglecting their inner states. The opposite is true for synchronization which focuses on the internal dynamics of oscillators rather than motion. Synchronization and swarming both involve large groups of individuals that self-organize and interact following simple rules. Synchronization and swarming are both at the intersection of nonlinear dynamics ands statistical physics. The two fields have been brought together through studies of “mobile oscillators”, which have applications in robotics and developmental biology.

Swarmalators are hypothetical systems for mobile oscillators where there is a bidirectional coupling between spatial and phase dynamics. For example, myxobacteria modeled by Igoshin and colleagues in 2001 may represent a swarmalator system. The bacteria movement in space are believed to be influenced by cyclically varying biochemical degree of freedom, which the researchers modeled as a phase oscillator. Since experimental evidence suggests that the spatial density of neighbouring cells influences the evolution of this phase, there is an apparent bidirectional coupling between spatial and phase dynamics, fitting with a swarmalator system.

Steven Strogatz and Keven O’Keeffe at the Center for Applied Mathematics, Cornell University are authors a Nature publication in 2017 that introduced the term swarmalator. Their research was inspired by the mating ritual of male Japanese tree frogs which form patterns in space and time because the males avoid being situated next to another that is croaking at the same time. The animals attempt to croak in anti-phase, so one croaks while the other is silent.

The Cornell research group used a pair of governing equations to demonstrate five swarmalator states: static synchrony, static asynchrony, static phase wave, splintered phase wave and active phase wave. Static synchrony has circular symmetry, crytal-like distribution and fully synchronized in phase. Static asynchrony shows uniform distribution where every phase occurs everywhere. Static phase wave is when swarmalators settle near others in a similar phase to their own. Splintered phase wave is characterised by nonstationary, disconnected clusters of distinct phases. Active phase wave is a state of similar to biodirectional states where populations split into counter-rotating subgroups, similar to vortex arrays formed by groups of sperm.


Applications for swarmalators in robotics (swarmalatorbots) are described by Gniewek, Barcis and Bettstetter from University of Klagenfurt in arXiv in 2019. The researchers adapted and extended the model for mobile robots in their Robot Operating System 2 (ROS 2). The group demonstrate that theoretical space-time patterns can be reproduced in practice and propose applications for swarmalators in robot monitoring, and exploration as well as art and entertainment. Applications for swarmalators have also been proposed for autonomous transport systems, self-configuring antenna arrays and planning of factory processes.

Magnetic domain walls, objects whose dynamics is connected to their structure, have been viewed as swarmalators through studying thin magnetic bilayers. The study was published by researchers at Université Paris-Saclay and Institut Néel at CNRS (Le Centre national de la recherche scientifique) in France.




Further reading


A review of swarmalators and their potential in bio-inspired computing

Kevin O'Keeffe, Christian Bettstetter

Mathematician's study of 'swarmalators' could direct future science


Oscillators that sync and swarm


Documentaries, videos and podcasts


Robots that sync and swarm: A proof of concept in ROS 2




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