A Model for the Periodic Synaptic Inhibition of a Neuronal Oscillator

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Abstract
We develop a simple, piecewise linear differential equation with discontinuous jumps, which captures the essential chracterstics of more complicated equations modelling the dynamics of neuronal oscillators, such as those due to Hodgkin & Huxley (1952), Fitzhugh (1960, 1961), and Nagumbo et al. (1962). We investigate the effects of peridically applied stimuli of various durations ande compare phase-transition curves or Poincaré maps for our model with numerically computed maps from the ‘full’ equations. We describe some aspects of the qualitative behaviour and bifurcations of these iterated one-dimensional mappings and attempt to relate them to experimental observations.