The main parts of the central olfactory system are the bulb (OB), anterior nucleus (AON), and prepyriform cortex (PC). Each part consists of a mass of excitatory or inhibitory neurons that is modelled in its noninteractive state by a 2nd order ordinary differential equation (ODE) having a static nonlinearity. The model is called a KOe or a KOi set respectively; it is evaluated in the "open loop" state under deep anesthesia. Interactions in waking states are represented by coupled KO sets, respectively KIe (mutual excitation) and KIi (mutual inhibition). The coupled KIe and KIi sets form a KII set, which suffices to represent the dynamics of the OB, AON, and PC separately. The coupling of these three structures by both excitatory and inhibitory feedback loops forms a KIII set. The solutions to this high-dimensional system of ODEs suffice to simulate the chaotic patterns of the EEG, including the normal low-level background activity, the high-level relatively coherent "bursts" of oscillation that accompany reception of input to the bulb, and a degenerate state of an epileptic seizure determined by a toroidal chaotic attractor. An example is given of the Ruelle-Takens-Newhouse route to chaos in the olfactory system. Due to the simplicity and generality of the elements of the model and their interconnections, the model can serve as the starting point for other neural systems that generate deterministic chaotic activity.