Rather than a single phenomenon, epileptic activity in the brain consists of a sequence of events – onset, propagation, and termination. Each component can be understood both biologically and mathematically as distinct and independent dynamic processes. Of the three steps, one could argue that understanding the onset, or ictogenesis, of epilepsy is of primary importance. That is, if we can understand and control how epileptic seizures begin, we may be able to find a means to stop them even before they start. Intuitively, ictogenesis is easy to understand. A group of errant neurons become active and recruits activity in other neurons until the neuronal network reaches some threshold and explodes into uncontrolled activity. Describing the same process with mathematical rigor is more problematic. What do we mean by "network threshold"? How does one describe an unstable manifold in a network of spiking neurons? Does the relevant dynamic variable depend on the number of active neurons or on the temporal pattern of activity between them? In this presentation, we describe our initial steps toward answering these questions. We will present data from an experimental model of epilepsy using brain slices. These data provide clues for understanding the biology of a network-based unstable manifold separating the rest state from epileptiform activity. We then frame the problem of ictogenesis mathematically using three strategies. First, we will present results from large-scale network models that capture the ictogenic process observed experimentally. Next, we will present a reduced model that illustrates how we can relate biological data to a linear stability analysis of network threshold. Finally, we propose the use of the Globally Coupled Map (GCM) framework as a vehicle for a full stability analysis of activity in a network of spiking neurons.