Which center bears the primary responsibility for generating the respiratory rhythm, but is influenced by several other centers

This is the Ventral Regulatory Group-VRG

Explanation:

In the medulla,there are four groups of neurons which forms the exhalation parts of the   respiratory  control.These 4 groups are called the VRG.They occupy 5mm anterior in length, and laterally positioned to the dorsal respiratory group.They are therefore said to occupy the ventrolateral part of the medulla.

The dorsal respiratory group(DRG) consists of the inspiration neurons,contrary to the VRG. They do not extend to the DRG,but the DRG, extends to them

They(VRG) function in propagating action potentials needed for the mechanisms of respiration.(exhalations), and Inspirations

the cladogram shown here shows similarities and differences among several classes of vertebrates. anatomically, the four have limb structure as their common ancestor. we might separate the mammals from the other three classes because they a) divergent; do not lay eggs b) identical; are warm-blooded c) varied; a four chambered heart d) homologous; have mammary glands