A neuron field theory: Mathemalical approaches to the problem of large numbers of interacting nerve cells
✍ Scribed by Burkhart Fischer
- Publisher
- Springer
- Year
- 1973
- Tongue
- English
- Weight
- 524 KB
- Volume
- 35
- Category
- Article
- ISSN
- 1522-9602
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✦ Synopsis
A field theoretical approach to the problem of continuously distributed and simultaneously active nerve cells is presented, starting with a differential-integral field equation of the form
~¢(r, t) = He(r, t) + F(r, ~)
which relates the field ~b to its inhibitory and excitatory sources 2' by means of the field operator H. General solutions are represented with the aid of Green's functions. The Green's function, giving the response of the system to a very short point stimulation, is calculated in the absence of interaction between neurons and for a special case of non-local interaction. Possible applications of the theory are demonstrated for receptive fields and neuronal mechanisms in the vertebrate retina.