Mathematical model of non-basal testosterone regulation in the male by pulse modulated feedback

A parsimonious mathematical model of pulse modulated regulation of non-basal testosterone secretion in the male is developed. The model is of the third differential order, reflecting the three most significant hormones in the regulation loop, but is yet shown to be capable of sustaining periodic solutions with one or two pulses of gonadotropin-releasing hormone (GnRH) in each period. Lack of stable periodic solutions is otherwise a main shortcoming of existing low-order hormone regulation models. Existence and stability of periodic solutions are studied. The periodic mode with two GnRH pulses in the least period has not been described in medical literature, but is found to explain experimental data well.