Phase-locking patterns underlying effective communication in exact firing rate models of neural networks
Fig 3
Rotation numbers and phase-locking regions for the forced PING oscillation varying input parameters.
(A) Temporal evolution of firing rate, mean membrane potential and synaptic variables over a cycle of a PING oscillation for system (1)-(2) corresponding to the red cross in Fig 2A. (B) Infinitesimal Phase Response Curve (iPRC) for perturbations in the direction of the variables Ve and Vi (red and blue curves, respectively) and the sum of them (purple curve). (C) Von Mises (circular) distribution as a function of the factor κ controlling the input coherence. Large values of κ result in distributions concentrated around the location μ = 0, whereas smaller values lead to broader low-amplitude distributions. The black horizontal line corresponds to the uniform distribution (limit case attained when κ = 0). (D, E) Rotation numbers of the stroboscopic map (9) for a von Mises input (15) applied in the direction of Ve and Vi, as a function of the ratio between the intrinsic period of the E-I network T* and the input period T. (D) Rotation numbers for κ = 2 and different amplitude values A. (E) Rotation numbers for A = 0.1 and different input coherence values κ. (F) Arnold tongues computed using the phase reduction corresponding to the 1:1 (orange), 1:2 (purple) and 2:1 (blue) phase-locked states for different input coherence: κ = 20, 2, 0.5 corresponding to the regions delimited by solid, dashed, dash-dotted curves, respectively. In grey, we show the corresponding Arnold tongues for pulsatile inputs (κ → ∞) obtained analytically. See Methods.