Dynamical behavior of a pacemaker neuron model with fixed delay stimulation

In physiological and pathological conditions, many biological oscillators, such as pacemaker cells, operate under the influence of feedbacks. Fixed delay stimulation is a standard preparation to evaluate the effects of such influences. Through the study of the Hodgkin-Huxley model, we show that such recurrent excitation can lead to regular and irregular discharge trains with interdischarge intervals that are up to several multiples of the period of the oscillator. In other words, we show that recurrent excitation can considerably slow down the firings of the pacemaker. This result contrasts with previous studies of similar preparations that have reported that fixed delay stimulation leads to a bursting pattern in which regimes of high-frequency firing alternate with periods of quiescence. We elucidate the mechanisms underlying the behavior of the oscillator under fixed delay perturbation through the analysis of the dynamics of a well-known two-dimensional oscillator, namely, the Poincaré oscillator.