We study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type couplings, where the phase interactions are governed by phase differences. Here we consider Winfree-type coupling, where the interactions are multiplicative, determined by the product of a phase response function $Q\left(\theta \right)$ and phase pulse function $P\left(\theta \right)$. This more general interaction (from which the Kuramoto phase differences emerge after averaging) produces rich physics: six long-term modes of organization are found, which we characterize numerically and analytically.

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• Collective dynamics
• Coupled oscillators
• Synchronization