Summary Fertility critically depends on the gonadotropin-releasing hormone (GnRH) pulse generator, a neural construct comprised of hypothalamic neurons co-expressing kisspeptin, neurokoinin-B and dynorphin that drives the pulsatile release of GnRH. How this neural network generates and controls the appropriate ultradian frequency essential for gametogenesis and ovulation is unknown. Here, we present a mathematical model of the GnRH pulse generator with theoretical evidence and in vivo experimental data showing that robust pulsatile release of luteinizing hormone, a proxy for GnRH, emerges abruptly as we increase the basal activity of the neuronal network using continuous low frequency optogenetic stimulation of the neural construct. Further increases in basal activity markedly increase pulse frequency. Model predictions that such behaviors are concomitant of non-linear positive and negative feedback interactions mediated through neurokinin-B and dynorphin signaling respectively are confirmed neuropharmacologically. Our mathematical model sheds light on the long-elusive GnRH pulse generator offering new horizons for fertility regulation.