Origin of attractor fatness in the collective-oscillation regime

Determine whether the broad attractor observed during collective oscillations in the massively coupled Erdős–Rényi excitatory–inhibitory spiking network with short‑term synaptic depression acting on excitatory‑to‑excitatory synapses arises from finite‑size effects or indicates intrinsic high‑dimensional dynamics. Concretely, ascertain the cause of the wide oscillatory attractor seen when varying time scales (e.g., decreasing the depression time constant to τ_d = 0.1 s) by distinguishing finite‑size artifacts from genuine high‑dimensional behavior.

Background

In the Supplementary Material, the authors report that varying certain time scales (e.g., the synaptic depression time constant) can induce collective oscillations in their two‑population spiking neural network model with short‑term synaptic depression on excitatory‑to‑excitatory connections. Under these conditions, scatter plots of inhibitory versus excitatory fields display a relatively wide oscillatory attractor compared to the asynchronous regime.

The authors note that the attractor appears suggestive of underlying low‑dimensional dynamics, but emphasize that their simulations at only one (or a few) network sizes are insufficient to determine whether the observed fatness of the attractor is due to finite‑size effects or reflects intrinsic high‑dimensionality. This leaves open the methodological and theoretical question of how to characterize the attractor's dimensionality and the origin of its geometry in the stated model regime.