The cornerstone bifurcation generates mechanisms controlling bursting in neural networks. (A). Two endogenously silent, mutually inhibitory coupled neurons produce alternating bursting activity. V1/2,mk2 controls BDs. (B). The BDs are depicted as blue dots. The curve fit for BDs took the form b/. (C). Two endogenously spiking, mutually inhibitory coupled neurons produce synchronous bursting activity. V1/2,mh controls IBIs. (D).Curve fit for IBIs took the form b/. The curves fitted to these data are depicted in red.