Before revision:  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 .
After revision:  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 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 .