A mathematical model of the mechanism of olfaction has been developed in the form of coupled nonlinear integrodifferential equations. The model was first constructed to simulate the performance of the separated bulb or cortex in response to electrical impulse stimulation of its input and output nerves. With sufficiently high internal feedback gains, the model entered a stable limit cycle state at frequencies characteristic of the EEG bursts. The instability was diminished when the connection densities and input amplitude were spatially nonuniform, though these factors could be compensated by increasing the internal gains (connection strengths). This model failed to simulate three important characteristics of olfactory activity: (1) the dependence of spatial patterns of bulbar output on internal connectivity rather than on input patterns; (2) the exquisite selective sensitivity of the bulb to learned inputs; and (3) its broad spectrum and aperiodic wave forms. The model was changed by including an asymmetric sigmoid nonlinearity, and by introducing long feedback connections from the cortex to the bulb that had dispersive delays. These changes sufficed to provide chaotic solutions of the equations, and to selectively sensitize the system to destabilization by input, thereby improving the simulations of the biological activity. The conclusion is put forth that for pattern recognition to be done, the chaotic activity of the sensory system must arise from a macroscopic attractor. Local fluctuations are everywhere damped by the distributions of return times and strengths owing to biological variability in neuron size and connection density. Thus high-dimensional local stability is combined with low-dimensional global instability, so as to emphasize the relationships among local features in a holistic sensory input pattern.