Gonadotropin-releasing hormone (GnRH) neurons are hypothalamic neurons that control the pulsatile release of GnRH, which in turn governs fertility and reproduction in mammals. Although the mechanisms underlying the pulsatile release of GnRH are not well understood, it has been suggested that the bursting behavior of electrical activity and calcium (Ca2+) dynamics in GnRH neurons could play important roles in GnRH secretion. Previous studies have shown that some of the mechanisms for controlling electrical bursting are located in the soma of the GnRH neuron. Furthermore, GnRH neuron projections have the properties of both dendrites (which receive synaptic inputs from other neurons) and axons (which are the site of action potential initiation and propagate action potentials to the synaptic terminal). These observations raise two important questions: How can electrical bursting be controlled when it is initiated at a site located some distance (often more than 100 mm) from the controlling mechanisms? More specifically, how do the soma and the site of action potential initiation interact to control the electrical bursting? How does stochastic synaptic input along the dendrite affect the initiation and propagation of action potentials? We constructed a spatiotemporal mathematical model of a GnRH neuron that includes both the soma and the dendrite. The most important new parameter introduced in this model, the electrical diffusion coefficient, was determined by fitting to experimental data. The model shows that a large diffusion coefficient provides a mechanism for regulating bursting behavior through interactions of the soma and the site of action potential initiation. In order to study the function of synaptic input along the dendrite, we extended our spatiotemporal model by adding stochastic synaptic input. We demonstrated that synaptic input along the dendrite is not a likely mechanism for controlling action potential propagation in the dendrite or GnRH secretion. We thus investigated other possible ways in which extrinsic input could modify Ca2+ release at the synaptic terminal, focusing in particular on the possible role of kisspeptin. We concluded that the inherent synergies in the various actions of kisspeptin make it a likely candidate for the precise control of Ca2+ transients at the synaptic terminal, and hence a possible candidate for the control of long-period GnRH secretion.