  We propose a mathematical model allowing for the alternating pulse and surge
pattern of GnRH (Gonadotropin Releasing Hormone) secretion. The model is based
on the coupling between two systems running on different time scales. The
faster system corresponds to the average activity of GnRH neurons, while the
slower one corresponds to the average activity of regulatory neurons. The
analysis of the slow/fast dynamics exhibited within and between both systems
allows to explain the different patterns (slow oscillations, fast oscillations
and periodical surge) of GnRH secretion. Specifications on the model parameter
values are derived from physiological knowledge in terms of amplitude,
frequency and plateau length of oscillations. The behavior of the model is
finally illustrated by numerical simulations reproducing natural ovarian cycles
and either direct or indirect actions of ovarian steroids on GnRH secretion.
