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

TL;DR

This study addresses whether explosive synchronization (ES) is a universal feature of Type-I neuronal networks by exploiting a mapping to the Kuramoto model. It analyzes electrically coupled networks on scale-free and star topologies using both the normal-form $QIF$ model and biophysical Morris–Lecar neurons under weak heterogeneity and various degree-frequency correlations. The key finding is that ES occurs under complete and partial degree-frequency correlations, with hysteresis and sharp transitions, and that uncorrelated degrees yield continuous transitions; backward transition points align with Kuramoto predictions. This work broadens the applicability of ES to a broad class of Type-I neurons and provides a unified framework for abrupt brain synchronization phenomena.

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.

Figures (6)

• Figure 1: A sharp transition to synchronization accompanied by hysteresis in the order parameter is seen for a scale-free network of 1000 QIF neurons with complete degree-frequency correlation. $\gamma = 2.4$ (black line) and $\gamma =2.7$ (red line). For both cases $\bar{\eta} = 20$, $\varepsilon = 0.01$ with solid curves representing forward simulations and dotted lines representing backward simulations.
• Figure 2: Plots of 1000 QIF neurons connected by an SF network with varying degree-frequency correlations. In all cases, the same SF network with $\gamma = 2.3$ is used. (a) Complete degree-frequency correlation. (b) Only the top $10 \%$ of neurons with the highest degree are assigned frequencies correlated with their degree, while the rest are assigned random frequencies. (c) All neurons are assigned random frequencies. In both (b) and (c), random frequencies are drawn from a Lorentzian distribution $p(k) = a/\pi((k-k_0)^2 - a^2)$ with $k_0 = 0$ and $a=1$. For all cases $\bar{\eta} = 20$ and $\varepsilon = 0.01$.
• Figure 3: Forward simulations of Star networks of QIF neurons with complete degree-frequency correlation. N is the number of neurons in the network. For these simulations $\bar{\eta} = 20$, $\varepsilon = 0.01$.
• Figure 4: Effect of $\varepsilon$ on the transition points in a 21 complete degree-frequency correlated star networks of QIF neurons. The solid lines represent the forward g simulation, while the dotted line represents the backward simulation. Other parameters are the same as in Fig. \ref{['fig2.5']}.
• Figure 5: Explosive synchronization along with Hysteresis in the order parameter for a scale-free network of 1000 Degree-frequency correlated ML neurons.$\gamma = 2.4$ (black line) and $\gamma =2.3$ (red line). For both cases, $I_{0} = 43.0$, $\varepsilon = 0.01$, and the solid curves represent the forward simulations while the dotted lines represent the backward simulations.