Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity
Fig 3
Up-down dynamics due to finite-size fluctuations.
Mesoscopic model reproduces noisy bistable population dynamics. (A) Phase-plane analysis of macroscopic dynamics (Eq (3) for N → ∞) reveals two stable fixed points (red): a high-activity focus representing the Up, and the low-activity node the Down state of the system. From the saddle fixed point (orange diamond), an unstable (orange dotted line) and a stable manifold (red dashed line) emerge. The latter acts as a separatrix—trajectories (blue curve) starting from above make an excursion around the unstable limit cycle (green dashed) and converge towards the down state. Finite-size fluctuations can make the trajectory cross the limit cycle into the basin of attraction of the Up state. (B,C) Stochastic trajectory of the mesoscopic dynamics (3) with N = 100 transitioning between Down and Up states. (D) The mesoscopic models with hybrid noise (jump-diffusion model; blue) and Gaussian noise (diffusion model; orange) qualitatively capture Up-Down-dynamics of the microscopic network (black). (E) Power spectrum and (F) histogram of input potential h over simulation of length Tsim = 100′000s. Model parameters can be found in Table 1.