Solitary states in spiking oscillators with higher-order interactions

We study a system of globally coupled FitzHugh-Nagumo oscillators with pairwise and second-order interactions, showing that the presence of higher-order interactions substantially affects the character of the transition between synchronous and asynchronous states driven by changes in coupling strength. In particular, we demonstrate that, around the synchronization transition, solitary states emerge due to the presence of second-order interactions. We also show that, in contrast to the phenomenology observed in systems of phase oscillators, at low fixed pairwise coupling strengths, solitary states appear for both transition directions as the second-order interaction strength is varied, whereas for higher couplings they only occur in the forward direction, with the backward one characterized by explosive desynchronization.