The olfactory bulb is the first central component in a highly sensitive yet markedly stable sensory system. It receives a surge of receptor activity with each inspiration and transmits output as a brief burst of oscillatory activity that is most clearly seen in the EEG. These properties together with the known anatomy and physiology of the bulb are used as design criteria to synthesize, evaluate and solve a set of nonlinear differential equations that represent lumped bulbar dynamics. According to the model bulbar processing is in two stages. In the outer layers the interneurons perform the operations of input range compression, integration, clipping, holding, and bias control. In the inner layers the input surge is converted to a burst, which is transmitted by the mitral cells as a pulse density wave. The phase, frequency, duration, and amplitude of the wave convey information centrally about both the input and the state of the system. The model suffices to replicate the forms of the EEG burst; the pulse probability distributions conditional on the EEG; the waveforms of averaged evoked potentials (AEPs) and post stimulus time (PST) histograms from the bulb and cortex; and the changes in waveform induced by behavioral control of attentiveness and habituation. It is inferred that with selective attention there is a permanent change in the strength of mutually excitatory connections among excitatory neurons, and that with habituation there is a reversible change in the effectiveness of excitatory synapses. The limitations and deficiencies of the model and the need for centrifugal controls of bulbocortical function are discussed.