# Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons

## TL;DR

This paper investigates the complex dynamics of two coupled populations of quadratic integrate-and-fire neurons, revealing various non-symmetric states and bifurcations through a novel reduction method validated by simulations.

## Contribution

It introduces an exact reduction method for analyzing coupled neuron populations with heterogeneous neurons, uncovering diverse dynamical patterns.

## Key findings

- Discovery of splay, antiphase, and chimera-like states.
- Identification of chaotic oscillations and bistabilities.
- Validation of the reduction method with numerical simulations.

## Abstract

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of non-symmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, also chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.