Hierarchy of chaotic dynamics in random modular networks

TL;DR

This paper explores the complex chaotic behaviors in hierarchical random modular neural networks, revealing how modularity and noise influence chaos and system stability through theoretical and simulation analyses.

Contribution

It introduces a hierarchical modular network model and analyzes its chaotic phases, showing how modularity and noise affect chaos attenuation and system dynamics.

Findings

Chaotic phases are separated by a crossover region with unique Lyapunov properties.

Adding noise or modularity can attenuate chaos unexpectedly.

Hierarchical connectivity drives the system towards the edge of chaos.

Abstract

We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic phases, separated by a crossover region characterized by low values of the maximal Lyapunov exponent and participation ratio dimension, but with high values of the Lyapunov dimension that change significantly across the region. Counterintuitively, chaos can be attenuated by either adding noise to strongly modular connectivity or by introducing modularity into random connectivity. Extending the model to include a multilevel, hierarchical connectivity reveals that a loose balance between activities across levels drives the system towards the edge of chaos.