  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.
