Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions

TL;DR

This paper investigates how delayed, partially anti-symmetric interactions in large randomly connected networks induce a novel bifurcation leading to a heterogeneous oscillatory state where individual units oscillate without population-level oscillations.

Contribution

It identifies a new bifurcation mechanism in high-dimensional networks caused by delays and anti-symmetry in interactions, leading to heterogeneous oscillations.

Findings

Discovered a bifurcation where eigenvalues cross at non-zero frequency due to delays.

Heterogeneous oscillatory states emerge with individual unit oscillations.

Oscillations are not visible at the population-average level.

Abstract

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks consisting of randomly coupled rate units. We identify a novel type of bifurcation in which a continuous part of the eigenvalue spectrum of the linear stability matrix crosses the instability line at non-zero-frequency. This bifurcation occurs when the interactions are delayed and partially anti-symmetric, and leads to a heterogeneous oscillatory state in which oscillations are apparent in the activity of individual units, but not on the population-average level.