FIG. 2.
Generation of the 3-phase respiratory pattern in the intact model. A: traces of model output activities for all 4 neurons. B: mathematical representation of the “bio” 3-phase pattern, projected to (V1, V2, V3). During the early-inspiratory (early-I), postinspiratory (post-I), and augmenting expiratory (aug-E) phases, the solution trajectory follows curves of fast subsystem equilibria (dark solid curves). When transition surfaces are reached (red curves denote one-dimensional bifurcation curves within these surfaces), fast jumps between equilibrium surfaces occur (blue dashed curves, arrows), indicating transitions between phases of activity. Light blue curves show curves of unstable equilibria of the fast subsystem for the vectors (hNaP, mAD2, mAD3, mAD4) that arise along each fast jump. Each curve of unstable equilibria eventually connects with a curve of stable equilibria (green curves) at a fold point. C: the solution trajectory (solid) projected to (mAD2, mAD3) space consists of an inspiratory phase of increasing mAD2 and an expiratory phase of decreasing mAD2; fast jumps do not appear since mAD2, mAD3 are essentially constant along these jumps. Arrows show direction of time evolution. Transitions occur at bifurcation curves (dashed, inspiration-to-expiration or I-to-E; dash-dotted, expiration-to-inspiration or E-to-I). The E-to-I transition curve features 2 components, one corresponding entirely to escape from inhibition (escape) and the other to a combination of release and escape (release); see text for further details.