Diagram of the preBötC, intermediate reticular formation, and XII nucleus, which generate inspiratory-related rhythm and motor output, respectively. A, The preBötC network (bottom lozenge) consists of 250 neurons. Some preBötC neurons (set B) are allowed to connect to the reticular formation premotor system (middle lozenge), 50 preBötC neurons (set A) directly connect to model XII nucleus to influence fictive nerve output. The rest of the preBötC neurons only connect within the preBötC (set C). All preBötC neurons (sets A–C) are allowed to connect to each other with a fixed connection probability. The reticular premotor system consists of 100 neurons (set D) that all project to the model XII nucleus. Circles represent neuron populations. Lines with round terminations indicate directed synaptic projections. Synaptic projections among neurons within the same population are indicated by a recurrent connection (e.g., the line projecting from set A back into set A). Interconnection between the preBötC and the reticular premotor system is either Erdős-Rényi (random) or obeys an antipreferential attachment rule. The synaptic interconnection for constituent neurons of the reticular premotor system is either Erdős-Rényi, scale-free, or small-world (set D). Specific connection topologies are not accurately represented in this schematic, which rather shows a basic schematic of the whole system. We also show three diagrams representing three characteristic networks: Erdős-Rényi (A, right top), scale-free (A, right middle), and small-world network (A, right bottom), respectively. B, Interconnection between model preBötC and reticular premotor networks as a function of the allowable fraction (i.e., the fixed proportion of preBötC neurons that may connect to reticular premotor neurons) and probability that they do so. Blocks show the number of synchronized premotor neurons according to the colorimetric scale (top) for one 30 s simulation. No simulated deletions were performed. *Indicates the parameter pair (0.36, 0.25) that ensures full synchronization of constituent premotor neurons.