Abstract
A stochastic model is proposed for a neuron which has an inhibitory stream interacting pre-synaptically with an excitatory stream. Uninhibited excitatories have a post-synaptic effect of increasing the membrane potential by random amounts, with the potential decaying linearly to zero in the absence of inputs. When the potential reaches a threshold level, the neuron fires. The Laplace transform of the probability density function of the interval between two successive firings is derived. The mean and the variance are obtained for exponential inter-arrival times and inputs as an example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bishop, P. O., Levick, W. R., Williams, W. O.: Statistical analysis of the dark discharge of lateral geniculate neurons. J. Physiol. (Lond.) 170, 598–612 (1964)
Clay, J. R., Goel, N. S.: Diffusion models for firing of a neuron with varying threshold. J. Theor. Biol. 39, 633–644 (1973)
Coleman, R., Gastwirth, J. L.: Some models for interaction of renewal processes related to neuron firing. J. appl. Prob. 6, 38–58 (1969)
Cox, D. R.: Renewal theory. London: Methuen (1962)
Eccles, J. C.: The physiology of synapses. New York: Academic Press 1964
Eyzaguirre, C.: Physiology of the nervous system. Chicago: Year Book Medical Publishers 1969
Knight, B. W.: Dynamics of encoding in a population of neurons. J. gen. Physiol. 59, 734–766 (1972)
Ochs S.: Elements of neurophysiology. New York: Wiley 1965
Roy, B. K., Smith, D. R.: Analysis of the exponential decay model of the neuron showing frequency threshold effects. Bull. math. Biophys. 31, 341–357 (1969)
Srinivasan, S. K.: Analytic solution of a finite dam governed by a general input. J. appl. Prob. 11, 134–144 (1974)
Srinivasan, S. K., Rajamannar, G.: Selective interaction between two independent stationary recurrent point processes. J. appl. Prob. 7, 476–482 (1970)
Stein, R. B.: The stochastic properties of spike trains recorded from nerve cells. In: Lewis, P. A. W. (Ed.): Stochastic point processes: Statistical analysis, theory and applications. New York: Wiley Interscience 1972
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
Additional information
Department of Mathematics
Biomedical Engineering Division, Department of Applied Mechanics
Rights and permissions
About this article
Cite this article
Srinivasan, S.K., Sampath, G. A neuron model with pre-synaptic deletion and post-synaptic accumulation decay, and threshold behaviour. Biol. Cybernetics 19, 69–74 (1975). https://doi.org/10.1007/BF00364103
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00364103