Early olfactory pathway responses to the presentation of an odor exhibit remarkably similar characteristics across phyla from insects to mammals, and frequently involve transitions among quiescence, collective network oscillations, and asynchronous firing. We investigate whether a robust bifurcation structure can describe such transitions, and take the locust, which appears to have one of the simpler early olfactory pathway architectures, as a representative example. Using an integrate-and-fire (I \& F) model , we reproduce relevant results of both experimental measurements and detailed models of early olfaction dynamics and odor discrimination. By further idealizing the I\&F description and finally reducing it to a firing-rate (FR) model , we find the bifurcation structure underlying a transition typical of the early odor response to be a slow passage through a saddle-node-on-an-invariant-circle (SNIC) bifurcation , which arises due to the interaction among the fast-varying excitation and fast and slowly-varying inhibition .
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 (I F) 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 (FR) model and use it to extract a slow passage through a saddle-node-on-an-invariant-circle (SNIC) 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 .
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investigate whether a robust bifurcation structure can describe such transitions, and take the locust, which appears to have one of the simpler early olfactory pathway architectures, as a representative example. Using an
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
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, we reproduce relevant results of both experimental measurements and detailed models of early olfaction dynamics and odor discrimination. By further idealizing the I\&F description and finally reducing it to
to verify this hypothesis via numerical simulations. To better understand the mathematical structure underlying the common dynamical behavior across species, we derive
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, we find the bifurcation structure underlying a transition typical of the early odor response to be
and use it to extract
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, which arises due to the interaction among the fast-varying excitation and fast and slowly-varying inhibition
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