Network mechanism for insect olfaction.

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Early olfactory pathway responses to the presentation of an odor exhibit remarkably similar dynamical behavior across phyla from insects to mammals, and frequently involve transitions among quiescence, collective network oscillations, and asynchronous firing. We hypothesize that the time scales of fast excitation and fast and slow inhibition present in these networks may be the essential element underlying this similar behavior, and design an idealized, conductance-based integrate-and-fire model to verify this hypothesis via numerical simulations. To better understand the mathematical structure underlying the common dynamical behavior across species, we derive a firing-rate model and use it to extract a slow passage through a saddle-node-on-an-invariant-circle bifurcation structure. We expect this bifurcation structure to provide new insights into the understanding of the dynamical behavior of neuronal assemblies and that a similar structure can be found in other sensory systems.