Spike Frequency Adaptation in a Neuronal Cell
by
Allan Willms
University of Canterbury

We present a model of the Lateral Pyloric (LP) cell of the stomatogastric ganglion of the Pacific spiny lobster which displays the experimentally observed phenomenon of spike frequency adaptation. We briefly itemize two generic mathematical mechanisms in systems with two fast and one slow variable which can bring about a transition from oscillatory to stationary solutions in a manner consistent with the data, and determine the asymptotic behaviour of the firing frequency under each of the these mechanisms. The model seems to possess a third, more complex mechanism associated with a subcritical Hopf-homoclinic bifurcation. We characterize the firing frequecy for this case and show that the model, and to some extent, the real cell, exhibit spike frequency adaptation in accord with this mechanism.

Date received: June 24, 1998