Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

This article presents the results of an exploration of one two-parameter space of the Chay model of a cell excitable membrane. There are two main regions: a peripheral one, where the system dynamics will relax to an equilibrium point, and a central one where the expected dynamics is oscillatory. In the second region, we observe a variety of self-sustained oscillations including periodic oscillation, as well as bursting dynamics of different types. These oscillatory dynamics can be observed as periodic oscillations with different periodicities, and in some cases, as chaotic dynamics. These results, when displayed in bifurcation diagrams, result in complex bifurcation structures, which have been suggested as relevant to understand biological cell signaling.