Dynamic phenomena in the olfactory bulb

A mathematical model of the olfactory bulb is presented to study the dynamics of the bulbar information processing. A two level model is adopted to describe both neural activity and synaptic modifiability. The model takes explicitly into account the existence of lateral interactions in the mitral layer, and the synaptic modifiability of these connections. A series of bifurcation phenomena among fix points, limit cycle and strange attractors have been demonstrated. Chaos occurred only in the case of excitatory lateral connections. Coexistence between oscillation and chaos, and synaptic modification induced transition have also been found. The model attempts to demonstrate the associative memory character of the olfactory bulb. Odour qualities are coded in distributed spatial amplitude patterns. Differential equations for the mitral and granule cell activities have been supplemented by a continuous-time local learning rule. A nonlinear forgetting term and a selective decreasing term is added to the Hebbian learning rule. A learned odour can be recalled by a subset of the pattern. There is a strict restriction on the parameters: only those values can be admitted which generate physiologically justified activity signals.