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Dergiler / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2022 / Cilt: 12 - Sayı: 2

A numerical scheme for the one-dimensional neural field model

Aytül Gökçe
Burcu Gürbüz
Sayfa
184–193
Yayın Tarihi
2022-10-11
DOI
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On the other hand, numerical results are obtained by the algorithm.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tis- sue in mathematical neuroscience.
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Temel Bulgular & Veri:Studying these models with a sigmoidal fir- ing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectiv- ities.
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Sonuç & Katkı:On the other hand, numerical results are obtained by the algorithm.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tis- sue in mathematical neuroscience. Studying these models with a sigmoidal fir- ing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectiv- ities. Because of the convolution structure of these integrals, it is possible to evaluate neural field model using a pseudo-spectral method, where Fourier Transform (FT) followed by an inverse Fourier Transform (IFT) is performed, leading to an identical partial differential equation. In this paper, we revisit a neural field model with a nonlinear sigmoidal firing rate and provide an efficient numerical algorithm to analyse the model regarding finite volume scheme. On the other hand, numerical results are obtained by the algorithm.

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Bu Makaleye Atıf Yap

Gökçe, A., Gürbüz, B. (2022). A numerical scheme for the one-dimensional neural field model. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 12 - Sayı: 2, 184–193. https://ajindex.com/articles/440521

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