Collective oscillations in balanced neural networks induced by discrete synaptic events

Authors: Denis S. Goldobin, Matteo di Volo, Alessandro Torcini

Presentation type: Poster at SNUFA 2024 online workshop (5-6 Nov 2024)

Abstract

Synaptic inputs in spiking neural networks have finite amplitude and are discrete, however mean field theories for these networks have been conventionally derived within the diffusion approximation, that approximates the synaptic inputs as a continuous Gaussian noise term. We derive a mean field formalism encompassing synaptic shot noise effects for a sparse balanced network of quadratic integrate-and-fire neurons. For highly sparse networks and low DC currents global oscillations emerge, as correctly predicted by our mean field approach, but not from the diffusion approximation. In particular, the inclusion of shot noise deeply modifies the diffusion phase diagram displaying sub- and super-critical Hopf bifurcations from asynchronous to oscillatory dynamics and a peculiar re-entrant Hopf bifurcation line for neurons weakly supra-threshold. Two collective oscillation regimes (for high and low in- degree) are shown to have different self-organization nature: drift-driven collective oscillations for sufficiently high in- degree (also possible with the diffusion approximation) and cluster-activation oscillations for low in- degree (impossible within the framework the diffusion approximation). These oscillations display frequencies in biologically relevant bands.