Periodic pulsatile stimulation of a nonlinear oscillator

We consider pulsatile periodic stimulation of an integrate-and-fire oscillator, and investigate the possible phase-locked patterns between the intrinsic rhythm and the forcing system. These stimulations are varied according to their period and intensity, corresponding to controllable experimental parameters. Phase transition curves are derived and analyzed under functional iteration. Two different perturbative mechanisms are considered, leading to significant differences in possible behaviors. Bistability can be obtained in one case. The analysis is reduced to the investigation of two-parameter families of discontinuous maps of the circle into itself.