Abstract: Oscillations in the membrane voltage of neurons have been widely studied at both the experimental and mathematical level. Depending on the specific type of neuronal network, the electrical activity may be periodic, or may display more complicated chaotic-like behavior. In this talk, I will give a very general overview of some of the computational abilities of neurons. I will then concentrate on a specific example involving a two-cell network. I will show how to derive a one-dimensional map whose dynamics, in some parameter regimes, completely predict the behavior of the two-cell network. In particular, I will show that as a certain parameter is varied, the network transitions through different kinds of periodic solutions some of which can be characterized using a countably infinite set of generalized Pascal Triangles. The main mathematical tools involve techniques from non-linear dynamics and geometric singular perturbation theory.