Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters

I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identical pairs. I use a simplified model for pancreatic beta-cells and decompose the system into fast (spike-generating) and slow subsystems to show how bifurcations of the fast subsystem affect bursting behavior. When coupling is weak, the spikes are not in phase but rather are anti-phase, asymmetric or quasi-periodic. These solutions all support bursting with smaller amplitude spikes than the in-phase case, leading to increased burst period. A key geometrical feature underlying this is that the in-phase periodic solution branch terminates in a homoclinic orbit. The same mechanism also provides a model for bursting as an emergent property of populations; cells which are not intrinsic bursters can burst when coupled. This phenomenon is enhanced when symmetry is broken by making the cells differ in a parameter.