Symmetry breaking and high-dimensional chaos in sparse random networks of exact firing rate models

TL;DR

This paper investigates the complex dynamics of neural population models on sparse random networks, revealing symmetry breaking and high-dimensional chaos through stability analysis and simulations.

Contribution

It introduces a comprehensive analysis of NG-NMMs on sparse networks, identifying conditions for various dynamical regimes including chaos and rhythmic states.

Findings

Inhibitory networks produce stationary patterns via winner-takes-all.

Directed networks exhibit high-frequency rhythmic states.

Simulations confirm high-dimensional chaos in certain regimes.

Abstract

Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity, multi-population models may display a range of different behaviors. In this work, we study the dynamics of all-excitatory or all-inhibitory NG-NMMs coupled through sparse random networks with row-normalized network topology. Linear stability analysis of the homogeneous states of the system, representing asynchronous neural activity, provides a dispersion relation linking the emergence of spatiotemporal dynamics to the spectra of the connectivity matrix. Using bounds from random matrix theory, we identify the parameter regions where instabilities occur. In undirected networks, only inhibitory systems produce heterogeneous stationary patterns, corresponding to a winner-takes-all mechanism. In directed networks, exotic rhythmic states with high frequencies emerge in both, excitatory and inhibitory systems. Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.