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Oscillatory dynamics are ubiquitous in biological networks. Possible sourcesof oscillations are well understood in low-dimensional systems, but have notbeen fully explored in high-dimensional networks. Here we study large networksconsisting of randomly coupled rate units. We identify a novel type ofbifurcation in which a continuous part of the eigenvalue spectrum of the linearstability matrix crosses the instability line at non-zero-frequency. Thisbifurcation occurs when the interactions are delayed and partiallyanti-symmetric, and leads to a heterogeneous oscillatory state in whichoscillations are apparent in the activity of individual units, but not on thepopulation-average level.

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