Phase-locking patterns underlying effective communication in exact firing rate models of neural networks
Fig 2
E-I cortical network with oscillatory activity in the gamma range.
(A) Two-parameter bifurcation diagram of system (1)-(2) for the excitatory current (x-axis) and the inhibitory current
(y-axis). The solid (resp. dashed) blue curve corresponds to a supercritical (resp. subcritical) Hopf bifurcation curve. Red circles correspond to (codimension 2) Generalized Hopf bifurcations (GH), also known as Bautin bifurcations. Purple curve corresponds to saddle node bifurcation of limit cycles. Green circle corresponds to a Cusp bifurcation of limit cycles (CPC), a point where two branches of saddle-node bifurcations of limit cycles meet tangentially. Oscillations occur in the blue and orange regions. Red cross corresponds to values
and
generating the limit cycle considered later on. (B, C) Frequency oscillation (green) and integral mean values of the firing rates re (dashed red) and ri (dashed blue) as a function of (B) tonic excitatory current
and (C) tonic inhibitory current
. See Eq (7). (D, E) Time difference (blue) and relative phase (orange) between inhibition and excitation as a function of (D) tonic excitatory current
and (E) tonic inhibitory current
. In Panels B and D the inhibitory current
is set to 0. In Panels C and E the tonic excitatory current
is set to 12. Other parameters are as in (6).