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Numerical solution of the stochastic neural field equation with applications to working memory

Author

Listed:
  • Lima, P.M.
  • Erlhagen, W.
  • Kulikova, M.V.
  • Kulikov, G.Yu.

Abstract

The main goal of the present work is to investigate the effect of noise in some neural fields, used to simulate working memory processes. The underlying mathematical model is a stochastic integro-differential equation. In order to approximate this equation we apply a numerical scheme which uses the Galerkin method for the space discretization. In this way we obtain a system of stochastic differential equations, which are then approximated in two different ways, using the Euler–Maruyama and the Itô–Taylor methods. We apply this numerical scheme to explain how a population of cortical neurons may encode in its firing pattern simultaneously the nature and time of sequential stimulus events. Numerical examples are presented and their results are discussed.

Suggested Citation

  • Lima, P.M. & Erlhagen, W. & Kulikova, M.V. & Kulikov, G.Yu., 2022. "Numerical solution of the stochastic neural field equation with applications to working memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    • Handle: RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122001741
    DOI: 10.1016/j.physa.2022.127166
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