Structural constraints on the emergence of oscillations in multi-population neural networks

TL;DR

This paper uses dynamical systems theory to identify structural conditions, such as the number of inhibitory nodes and connection strength, necessary for oscillations in neural networks, with implications for biological systems.

Contribution

It provides a rigorous proof of structural conditions for oscillations in threshold-linear networks, bridging theoretical results with biological observations.

Findings

An odd number of inhibitory nodes is necessary for oscillations.

Strong enough connections are required to generate oscillations.

Results reconcile experimental findings in basal ganglia with classical theories.

Abstract

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.