A modified radial isochron clock with slow and fast dynamics as a model of pacemaker neurons. Global bifurcation structure when driven by periodic pulse trains

A simple mathematical model of living pacemaker neurons is proposed. The model has a unit circle limit cycle and radial isochrons, and the state point moves slowly in one region and fast in the remaining region; regions can correspond to the subthreshold activity and to the action potentials of pacemaker neurons, respectively. The global bifurcation structure when driven by periodic pulse trains was investigated using one-dimensional maps (PTC), two-dimensional bifurcation diagrams, and skeletons involving stimulus period and intensity. The existence of both the slow and the fast dynamics has a critical influence on the global bifurcation structure of the oscillator when stimulated periodically.