Dynamics of Random Neural Networks with Bistable Units

TL;DR

This paper models a neural network with bistable units, revealing complex dynamics including long-lived chaos and phase transitions through simulations and mean-field analysis.

Contribution

It introduces a rate-based neural network model with bistable units and analyzes its dynamic regimes and phase transitions using theoretical and simulation methods.

Findings

Identification of bistable units due to strong self-interactions

Discovery of a regime with long-lived chaotic activity

Mapping of phase transitions in parameter space

Abstract

We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently strong, the self-interactions make the individual units bistable. Simulation results, mean-field calculations and stability analysis reveal the different dynamic regimes of this network and identify the locations in parameter space of its phase transitions. We identify an interesting dynamical regime exhibiting transient but long-lived chaotic activity that combines features of chaotic and multiple fixed-point attractors.