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Kybernetik

, Volume 15, Issue 1, pp 1–9 | Cite as

Improved neuronal models for studying neural networks

  • R. B. Stein
  • K. V. Leung
  • D. Mangeron
  • M. N. Oğuztöreli
Article

Abstract

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.

Keywords

Firing Rate Neuronal Model Neuronal Response Frequency Response Function Compute Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • R. B. Stein
    • 1
  • K. V. Leung
    • 1
  • D. Mangeron
    • 1
    • 2
  • M. N. Oğuztöreli
    • 1
  1. 1.Departments of Physiology, Computing Science and MathematicsUniversity of AlbertaEdmontonCanada
  2. 2.Polytechnic InstituteIasiRomania

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