Skip to main content

Stochastic neuronal models with realistic synaptic inputs and oscillatory inputs

  • Computational Models of Neurons and Neural Nets
  • Conference paper
  • First Online:
From Natural to Artificial Neural Computation (IWANN 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 930))

Included in the following conference series:

  • 777 Accesses

Abstract

The Poisson process driven stochastic models of the neural activity and their diffusion approximation are studied. Two main studies are presented here: stochastic models driven by nonhomogeneous Poisson process with oscillatory intensity, and double compartment model with realistic synaptic inputs. The “phase lock” and the “amplitude lock” behaviour was observed in the model with oscillatory inputs and strong dependence on the initial phase after reset the membrane potential. Introducing the realistic synaptic input to the stochastic models opens new class of neuronal models: it has significant influence on all statistic parameters and the model behaviour. The double compartment model with realistic synaptic inputs is able to produce the bursting activity and this mechanism is described.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bernard C., Ge Y. C., Stockley E., Willis J. B., Wheal H. V.: Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations, Biol. Cyb. 70, 267–273 (1994)

    Google Scholar 

  • Holden A. V.: Models of the Stochastic Activity of Neurons, Springer Verlag 1976

    Google Scholar 

  • Kloeden E. P., Platen E.: Numerical Solution of Stochastic Differential Equations, Springer Verlag 1992

    Google Scholar 

  • Lansky P., Rospars J. P., Valliant J.: Some Neuronal Models with Oscillatory Input, 1994

    Google Scholar 

  • Lansky P., Smith C. E., Ricciardi L. M.: One-dimensional stochastic diffusion models of neuronal activity and related first passage time problems, Trends in Biological Cybernetics 1

    Google Scholar 

  • Lewis P. A. W., Shedler G. S.:Simulation methods for Poisson processes in nonstationary systems, IBM research report 1978

    Google Scholar 

  • Longtin A., Bulsara A., Pierson D., Moss F.: Bistability and the dynamics of periodically forced sensory neurons, Biol. Cyb. 70, 569–578, 1994

    Google Scholar 

  • Musila M., Lansky P.: Simulation of a diffusion process with randomly distributed jumps in neuronal context. Int. J. Biomed Comput 31, 233–245, 1992

    PubMed  Google Scholar 

  • Musila M., Stochastic models of neuronal activity, Czech Technical University, PhD thesis 1990 (in Czech language)

    Google Scholar 

  • Tuckwell H. C., Richter W.: Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters, J. Theor. Biol 71, 167–183, 1978

    PubMed  Google Scholar 

  • Tuckwell H. C.: Synaptic transmission in a model for stochastic neural activity J. Theor. Biol 77, 65–81, 1979.

    PubMed  Google Scholar 

  • Tuckwell, H. C.: Stochastic Processes in Neurosciences, Monash university 1989

    Google Scholar 

  • Wilbur J. W., Rinzel J.: A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions J. Theor. Biol 105, 345–368, 1983.

    PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

José Mira Francisco Sandoval

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hruby, P. (1995). Stochastic neuronal models with realistic synaptic inputs and oscillatory inputs. In: Mira, J., Sandoval, F. (eds) From Natural to Artificial Neural Computation. IWANN 1995. Lecture Notes in Computer Science, vol 930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59497-3_186

Download citation

  • DOI: https://doi.org/10.1007/3-540-59497-3_186

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59497-0

  • Online ISBN: 978-3-540-49288-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics