Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions
Disordered Systems and Neural Networks
2016-12-21 v2 Neurons and Cognition
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.
Cite
@article{arxiv.1605.07977,
title = {Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions},
author = {Célian Bimbard and Erwan Ledoux and Srdjan Ostojic},
journal= {arXiv preprint arXiv:1605.07977},
year = {2016}
}