The bulletin of mathematical biophysics

, Volume 3, Issue 2, pp 63–69

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

  • Alston S. Householder

DOI: 10.1007/BF02478220

Cite this article as:
Householder, A.S. Bulletin of Mathematical Biophysics (1941) 3: 63. doi:10.1007/BF02478220


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.

Copyright information

© The University of Chicago Press 1941

Authors and Affiliations

  • Alston S. Householder
    • 1
  1. 1.The University of ChicagoChicagoUSA