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

Abstract: Explosive synchronization (ES), which was observed in the scale-free network of the Kuramoto model, 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 Type-I neurons and the Kuramoto model, 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 a 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, under weak heterogeneity. We further confirm this phenomenon in networks of Morris-Lecar neurons, in the regime of Type-I excitability, under similar conditions to the QIF neurons. Thus, this work establishes a set of universal conditions that allows ES to arise in Type-I neurons.