Modeling more realistic swarmalator behavior with pulsative interactions

Collective behavior in nature often involves two intertwined processes: spatial movement and rhythmic activity in time. Swarmalators exhibit both collective motion and synchronization, and represent a class of systems that has been the focus of a great deal of recent research. But most studies on swarmalators assume they are made up of identical agents interacting through continuous-type phase coupling.

In many real-world systems, such as fireflies flashing, Japanese tree frogs croaking, magnetic Janus particles, neurons firing, and in various engineered systems like drone swarms and wireless sensor networks, the agents communicate through brief, discrete pulses.

Ghosh et al. introduced a theoretical framework that takes swarmalator research a step forward by incorporating two major realistic features: pulsatile interactions (instead of sinusoidal coupling) and nonidentical agents that reflect real-world diversity. They embedded a traditional mathematical model for characterizing collective synchronization — the Winfree-type phase coupling model — into a one-dimensional ring model where each agent carries a distinct natural frequency.

“The analytical results demonstrate excellent agreement with numerical simulations, confirming the robustness of the theoretical framework,” said author Dibakar Ghosh. “The system exhibits several dynamical states that emerge in both spatially coherent (positive spatial coupling) and spatially incoherent (negative spatial coupling) regimes.”

Three of these states had yet to be revealed in swarmalator behavior until now.

“Overall, our study demonstrates that pulse-based coupling and heterogeneity fundamentally reshape the collective dynamics of swarmalators,” said Ghosh. “By bridging idealized mathematical models and realistic pulse-driven systems, the study provides deeper insight into how diversity and spatial modulation jointly govern synchronization and swarming in complex systems.”

Source: “Emergent dynamics in heterogeneous pulsatile swarmalators,” by Samali Ghosh, Kevin O’Keeffe, and Dibakar Ghosh, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0316053 .