  The olfactory system is constantly solving pattern-recognition problems by
the creation of a large space to codify odour representations and optimizing
their distribution within it. A model of the Olfactory Bulb was developed by Z.
Li and J. J. Hopfield Li and Hopfield (1989) based on anatomy and
electrophysiology. They used nonlinear simulations observing that the
collective behavior produce an oscillatory frequency. Here, we show that the
Subthreshold hopf bifurcation is a good candidate for modeling the bulb and the
Subthreshold subcritical hopf bifurcation is a good candidate for modeling the
olfactory cortex. Network topology analysis of the subcritical regime is
presented as a proof of the importance of synapse plasticity for memory
functions in the olfactory cortex.
