Dynamic equilibria and oscillations of a periodically stimulated excitable system

Regular instantaneous stimulation of a space-clamped, excitable system can result in a wide variety of responses, depending on the magnitude and frequency of stimulation in relation to the internal dynamics of the excitable system: (a) a one-one relationship between input stimuli and output pulses; (b) more than one input stimulus per output pulse, which occur at regular or irregular intervals; (c) complete abolition of pulses (what we term a ‘dynamic equilibrium’); (d) ‘super-pulses’ in which output pulses are combined. This paper illustrates some examples of such behaviour patterns, and outlines a discrete time-sampling framework which enables useful bifurcation diagrams to be constructed and equilibrium behaviour to be assessed.