Abstract
This paper discusses a neuronal model based on a model of Coleman and Gastwirth (1969). It is assumed that the excitatory input forms a Poisson process while the inhibitory input forms a stationary renewal process. The proposed interaction scheme is as follows: an inhibitor deletes at most N consecutive excitatory inputs and a response only occurs after the cummalative storage of M excitatory inputs. The Laplace transform of the probability density function (p.d.f.) of the inter-response intervals is derived together with results of the numerical inversions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bellman, R., Kalaba, R.E., Lockett, J.A.: Numerical inversion of the Laplace transform. New York: Elsevier 1966
Bishop, P.O., Levick, W.R., Williams, W.O.: Statistical discharge of lateral geniculate neurons. J. Physiol. (Lond.) 170, 598–612 (1964)
Coleman, R., Gastwirth, J.L.: Some models for interaction of renewal processes related to neuron firing. J. appl. Prob. 6, 38–58 (1969)
Ten Hoopen, M., Reuver, H.A.: Selective interaction of two independent recurrent processes. J. appl. Prob. 2, 286–292 (1965)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pooi, A.H., Lee, P.A. An interaction model of a poisson and a renewal process related to neuron firing. Biol. Cybernetics 17, 71–76 (1975). https://doi.org/10.1007/BF00363946
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00363946