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 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.

References in corpus (2)

• Transition to chaos in random neuronal networks
• Topological and Dynamical Complexity of Random Neural Networks

Cited by in corpus (3)

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• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations