A STATISTICAL MECHANICS OF NERVOUS ACTIVITY.

Abstract

A mathematical model is developed of the activity of nets of model nerve cells. A nonlinear operator is introduced to represent the transfer characteristics of nerve cells. This operator is a continuous function that represents the mean neural response to stimulating currents and voltages. The mathematics used is not the Boolean algebra of switching circuits, but differential equations. The dynamics of certain model neural circuits is examined, some of which are shown to exhibit undamped oscillatory responses to incoming signals. The techniques of Hamiltonian mechanics, equilibrium statistical mechanics, and Brownian motion theory are used to derive formulas for statistical features of the dynamics. A preliminary model is given for the existence of preferred states found in the firing patterns of neurons in animal nervous systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1969
Accession Number
AD0696684

Entities

People

  • Jack D. Cowan

Organizations

  • University of Chicago

Tags

DTIC Thesaurus Topics

  • Boolean Algebra
  • Brownian Motion
  • Cells
  • Circuits
  • Differential Equations
  • Equations
  • Mathematical Models
  • Mathematics
  • Mechanics
  • Models
  • Nerves
  • Nervous System
  • Neurons
  • Statistical Mechanics
  • Switching
  • Switching Circuits

Fields of Study

  • Biology
  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Neuroscience