ANTIPHASE, ASYMMETRIC AND APERIODIC OSCILLATIONS IN EXCITABLE CELLS .1. COUPLED BURSTERS

I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identi cal pairs. I use a simplified model for pancreatic beta-cells and deco mpose the system into fast (spike-generating) and slow subsystems to s how how bifurcations of the fast subsystem affect bursting behavior. W hen coupling is weak, the spikes are not in phase but rather are anti- phase, asymmetric or quasi-periodic. These solutions all support burst ing with smaller amplitude spikes than the in-phase case, leading to i ncreased burst period. A key geometrical feature underlying this is th at the in-phase periodic solution branch terminates in a homoclinic or bit. The same mechanism also provides a model for bursting as an emerg ent property of populations; cells which are not intrinsic bursters ca n burst when coupled. This phenomenon is enhanced when symmetry is bro ken by making the cells differ in a parameter.