Stochastic approximations of perturbed Fredholm Volterra integro-differential equation arising in mathematical neurosciences

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model, defined by a Fredholm Volterra integro-differential equation (FVIDE), which includes memory effects of the past in the propagation. Stochastic approximation and numerical simulations are discussed.

Original languageEnglish (US)
Pages (from-to)1173-1182
Number of pages10
JournalApplied Mathematics and Computation
Volume186
Issue number2
DOIs
StatePublished - Mar 15 2007
Externally publishedYes

Fingerprint

Volterra Integro-differential Equations
Integrodifferential equations
Neuroscience
Memory Effect
Stochastic Approximation
Wave propagation
Wave Propagation
Neurons
Neuron
Propagation
Data storage equipment
Numerical Simulation
Computer simulation
Model

Keywords

  • Error
  • Euler-Hermite method
  • Fredholm Volterra integro-differential equation
  • Neural network
  • Stochastic approximation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

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abstract = "This paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model, defined by a Fredholm Volterra integro-differential equation (FVIDE), which includes memory effects of the past in the propagation. Stochastic approximation and numerical simulations are discussed.",
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AU - Jackiewicz, Zdzislaw

AU - Welfert, Bruno

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KW - Neural network

KW - Stochastic approximation

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