Collective dynamics of pulse-coupled swarmalators

Collective motion in nature, from the murmurations of starlings to firefly flashes, showcases a remarkable level of self-organization. Swarmalator models are an emerging paradigm for describing collective behavior of oscillators which sync and swarm. Traditionally, most studies have focused on the self-organizing dynamics of swarmalators with continuous coupling. However, a key aspect of many biological systems, pulsed interactions, remains unexplored within the framework of swarmalators. In this paper, we analyze the collective behavior of pulse-coupled swarmalators with different characteristics of pulse and phase response curves. We report several collective states facilitated by the pulsatile interactions including bump state, active bump state, partial synchronized state, radial wave state, and death state. The stationary nature of spatial and phase dynamics characterizes the death state. Further, we provide an analytical estimate for the threshold coupling strength for the death state's existence by analyzing the minimal model's dynamics with two coupled swarmalators.