Instability to a heterogeneous oscillatory state in randomly connected   recurrent networks with delayed interactions
  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. 
C\'elian Bimbard, Erwan Ledoux, and Srdjan Ostojic
cond-mat.dis-nn q-bio.NC