title: Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions.
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 type of bifurcation in which a continuous part of the eigenvalue spectrum of the linear stability matrix crosses the instability line at nonzero frequency. This bifurcation occurs when the interactions are delayed and partially antisymmetric 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.
authors.affiliation: Laboratoire des Systèmes Perceptifs, Équipe Audition, CNRS UMR 8248, École Normale Supérieure, Paris, France.
authors.forename: Célian
authors.initials: C
authors.lastname: Bimbard
authors.affiliation: Group for Neural Theory, Laboratoire de Neurosciences Cognitives, INSERM U960, École Normale Supérieure-PSL Research University, Paris, France.
authors.forename: Erwan
authors.initials: E
authors.lastname: Ledoux
authors.affiliation: Group for Neural Theory, Laboratoire de Neurosciences Cognitives, INSERM U960, École Normale Supérieure-PSL Research University, Paris, France.
authors.forename: Srdjan
authors.initials: S
authors.lastname: Ostojic