Robustness of respiratory rhythm generation across dynamic regimes
Fig 6
Network oscillation mechanisms when pre-I is intrinsically oscillatory, with c11 = −0.03.
(A) Phase plane (hpre−I versus Vpre−I) for the pre-I unit. Black curve is the model output projected to this plane. Solid blue curves are Vpre−I-nullclines. The lower right nullcline corresponds to 0 inhibition to pre-I, the upper left nullcline (which continues out of the image) to the maximal inhibition received by pre-I (0.0965), and the middle nullcline to the inhibition level received by pre-I (0.09) when it begins its escape to the active phase by hitting the curve of knees (LK, grey dashed). The red curve is the hpre−I-nullcline, which is independent of inhibition level. The vertical black curve denotes the Vpre−I value at which the output of pre-I is half of its maximum value. Solid black circles and squares correspond to time points when inhibition to the pre-I unit is 0.09 and 0.0965, respectively. (B) Same solution projected to the plane in which the inhibition to pre-I is plotted versus hpre−I (black solid). As inhibition wears off, the trajectory first crosses the curve of pre-I fixed points (FP, green dashed) and then crosses the curve of Vpre−I-nullcline left knees (LK, blue dashed), allowing escape (black circle) and initiation of inspiration. Trajectories for reduced/increased inhibition from post-I to pre-I (b31 = 0.105/0.175) are also shown (dotted/dashed black). (C) Phase plane (hpost−I versus Vpost−I) for the post-I unit. Curves are analogous to those in (A). The Vpost−I-nullclines shown correspond to minimal inhibition to post-I (far right, inhibition is 0), occurring when the maximal value of Vpost−I is achieved along the trajectory (black square, same time point as in (A)); to maximal inhibition to post-I (far left, inhibition is 0.54); and to the inhibition level when pre-I initiates its escape (middle, inhibition is 0.0525, also marked by solid black circle at same time point as in (A)). (D) Phase plane (haug−E versus Vaug−E) for the aug-E unit. Curves are analogous to those in (A). From right to left, the Vaug−E-nullclines shown correspond to minimal inhibition to aug-E (inhibition is 0.05); to inhibition to aug-E at the moment when pre-I initiates its escape (inhibition is 0.0542, also marked by black circle at same time point as in other plots); to inhibition to aug-E when Vpre−I is at its peak (0.283); and to inhibition to aug-E when Vpost−I is at its peak (0.35, marked by black square at same time point as in other plots).