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States of the Olfactory Bulb
The plethora of everyday active states (waking, sleeping, etc.) have been reduced to four main states: (1) "open loop" (2) resting chaos, (3) oscillatory burst, (4) seizure. The states are listed in order of how much energy is used to sustain that state, with the "open loop" state using very little and seizure using the most. The difference in energy usage is most apparent in the comparison between amplitudes in a EEG diagram taken for each of the four states.

"open loop" -- deep anesthesia
Characterization: lack of background activity.
When perturbed with electrical stimulus the system quickly returns to rest without osciallation. This seems to indicate that the "open loop" state can be identified with a strong point attractor (very negative Liapunov constant).

resting chaos -- waking rest
Characterization: low-amplitude chaotic activity.
When perturbed with electrical stimulus the system falls into exponentially decaying oscillations appearing as a spiral inside the well of its potential (phase) portrait.
Potential-well portrait of resting chaos

Characterization: Extremely high amplitude spike activity.
Under several seconds of intense electrical stimulation an epileptic seizure is released. It is intiated after the failure of excitatory input transmission as shown by the decreasing responses at left to the last 5 pulses of the stimulus train. The seizure spike train then progressively emerges from a relatively quiet post-stimulus state. [1]

The "oscillatory burst" has been saved for last as it embodies the most interesting character -- complexity.

oscillatory burst -- inhalation
Characterization: limit cycle attractor.
The limit cycles formed by the oscillatory burst can be classified by their spatial parttern of amplitude modulation. These patterns have been found to correspond to specific stimulus odors. Thus, the scent of a mango and the scent of a banana will form recognizably different attractors. These attractors are latent during exhalation, but crystallize as a mosaic of basins during inhalation.
Below, the basins of attraction are realized as wells seated in the large, central peak of the potential (phase) portrait and associated section of bifurcation diagram.
Phase Portrait and Bifurcation Diagram of Inhalation
The basin which a stimulus will eventually fall (be attracted) into is determined by the odor stimulus.
The exhalation process acts as a sort of reset button, causing all attractors throughout the olfactory bulb to vanish.

I mentioned the word "complexity" above, I was using in both of its senses. First, the processes controlling the oscillations between the inhalation attractor and exhalation attractor are, indeed, complex in the sense that there is a rich field of connections making up the olfactory bulb neural network. Secondly, the system is complex in the sense that it lives on the boundary between chaotic and the periodic. This area, termed "complex" by Chris Langton, creator of Langton's ant, is said by him to be the zone in which life lives. In the area between the hostile and the boring.
Oscillation between inhalation and exhalation attractors.

[1] W. J. Freeman
Simulation of Chaotic EEG Patterns witha Dynamic Model of the Olfactory System
Biological Cybernetics. vol.56, pp.139-150, p.146. 1987.

Last modified: Tue Jan 4 09:23:44 PST 2000