Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

doi:10.1371/journal.pcbi.1009342

Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

Fig 9

PING oscillations close to a Hopf bifurcation.

(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 external current (close to the Hopf bifurcation curve in Fig 2A). (B) Infinitesimal Phase Response Curve (iPRC) of the cycle in Panel A for perturbations in the direction of the variables V_e and V_i (red and blue curves, respectively) and to both of them (purple curve). Note that the iPRC is both positive and negative. (C) Rotation numbers of the stroboscopic map (9) for a von Mises input (15) with coherence κ = 2 applied in the direction of V_e and V_i, as a function of the ratio between the intrinsic period of the E-I network T* and the input period T and different amplitude values A. (D, E, F) Time evolution of the mean firing rates of the E-cells (red) and I-cells (blue) along the unperturbed (dashed curves) periodic orbit for the system (1)-(2) and perturbed (solid curves) with the coherent von Mises input with A = 0.05 and relative frequency T/T*: (D) 0.9, (E) 1 and (F) 1.07. The period of the oscillators has been normalized to 1.

doi: https://doi.org/10.1371/journal.pcbi.1009342.g009