A neuronal model for the discharge patterns produced by cyclic inputs.

To understand the patterns of nerve impulses produced by sinusoidal stimuli, a simple model is considered which integrates input currents with a finite time constant until a threshold voltage is reached, whereupon an output pulse is produced and the process is restarted. We show here that (a) a general analytic solution exists for this model driven by sinusoidal stimuli, determining the interval between every member of the pulse train, (b) for all values of the parameters of the model a pattern exists which repeats periodically after a finite number of pulses in the absence of noise, (c) the system will approach a stable pattern which, if perturbed, will be recovered once the perturbation is removed, (d) the linear integrator or relaxation oscillator and the curren multiplier are limiting cases of this model.