Oscillations and Traveling Waves of Calcium: A Simplified Model

We construct a heuristic model of calcium oscillations in pancreatic acinar cells. The model is based on the two-state model of Sneyd et al. (Sneyd, J., A. LeBeau and D. Yule, 2000, Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis, Physica D, in press) and is similar in spirit to the FitzHugh reduction of the Hodgkin-Huxley equations. The simplifled model successfully reproduces the oscillatory behavior and wave behaviour of the more complex model. In particular, the simplifled model provides an example of a simple, physiologically relevant model that has a T-point and an associated spiral branch of homoclinic orbits.