Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity
Fig 2
Population spikes in excitatory populations of finite size.
(A) Phase-plane analysis of the macroscopic model (Eq (3) for N → ∞) reveals the backbone of the metastable dynamics due to the proximity of a separatrix (red-dashed) near the unique stable fixed point (red dot = cross-section of the black-dashed nullclines). Trajectories (blue) of the mesoscopic model reproduce population spikes by following the unstable manifold (orange dotted line) of the saddle fixed point (orange diamond). Population spikes have variable amplitude and inter-population spike intervals (ISI), see also (B,C). (D) The mesoscopic models with hybrid noise (jump-diffusion model; blue) and Gaussian noise (diffusion model; orange) accurately capture finite-size fluctuations in the input potential h—note the logarithmic y-scale—and population spikes of the microscopic network dynamics (black) of N = 30 neurons. (E) Power spectra of the input potential h and (F) ISI distributions coincide for all three models. (G-H) same as (D-F) for N = 200. Statistics are for simulations of length Tsim = 100′000s. Model parameters can be found in Table 1.