The bulletin of mathematical biophysics

, Volume 3, Issue 2, pp 63-69

First online:

A theory of steady-state activity in nerve-fiber networks: I. Definitions and preliminary lemmas

  • Alston S. HouseholderAffiliated withThe University of Chicago

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As an essay towards the determination of the effect of structural relations among nerve fibers upon the character of their activity, preliminary consideration is given to the steady-state activity of some simple neural structures. It is assumed as a first approximation that while acted upon by a constant stimulus, each fiber reaches a steady-state activity whose intensity is a linear function of the applied stimulus. It is shown by way of example that for a simple two-fiber circuit of inhibitory neurons knowledge of the stimuli applied to the separate fibers does not necessarily suffice to determine uniquely the activity that will result. On the other hand, there are deduced certain restrictions on the possible types of activity that may be consistent with a given pattern of applied stimulation.