Modeling the Network Dynamics of Pulse-Coupled Neurons

TL;DR

This paper develops a mean-field model for large pulse-coupled neuron networks, revealing how network topology influences collective dynamics and phase transitions efficiently.

Contribution

It introduces a reduced ODE system for analyzing large neuron networks with various degree distributions and correlations, improving computational efficiency.

Findings

Reduced model accurately predicts network dynamics for large sizes.

Degree distribution affects macroscopic behavior and synchronization.

Network assortativity influences the emergence of synchronized firing.

Abstract

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions, as well as degree correlations (assortativity). Using the ansatz of Ott and Antonsen (Chaos, 19 (2008) 037113), we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with scale-free degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations) we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.