Explosive synchronization in networks of type-I neurons with electrical synapses

Explosive synchronization (ES), which was observed in the scale-free network of the Kuramoto model [J. Gómez-Gardeñes et al., Phys. Rev. Lett. 106, 128701 (2011)], has been studied widely in the oscillator model. However, investigations of ES in neuronal networks, in spite of their importance in neuroscience, are limited and restricted to specific models. In this work, we explore the nature of the transition to synchronization in a class of neurons, namely, type-I neurons. Leveraging the mapping between networks of weakly heterogeneous type-I neurons and the Kuramoto model [P. Clusella et al., Chaos 32, 013105 (2022)] under weak coupling, we investigate whether the conditions known to induce ES in the Kuramoto model also do so in type-I neurons. The neurons are coupled through electrical synapses and placed on scale-free and star networks with complete and partial degree-frequency correlation conditions. Our simulations show ES in networks of Quadratic Integrate and Fire (QIF) neurons, the normal form of type-I neurons close to saddle node on invariant circle (SNIC) bifurcation, under weak heterogeneity. We further generalize this phenomenon to networks of type-I Morris-Lecar neurons, under conditions similar to those of QIF neurons. Thus, this work suggests conditions under which ES can arise in type-I neurons close to SNIC bifurcation under weak heterogeneity and weak electrical coupling.