A numerical scheme for the one-dimensional neural field model





Neural field, Integro-differential equation, Numerical methods


Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tissue in mathematical neuroscience. Studying these models with a sigmoidal firing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectivities. 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 a new 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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Author Biographies

Aytul Gokce, Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey

is a Research Fellow at Ordu University in Turkey, working in the broad area of applied mathematics. Aytül's research is mainly devoted to dynamical systems modelling in biology and medicine, and the understanding of patterning in real life problems.

Burcu Gurbuz, Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany

is a Research Associate in Johannes Gutenberg-University Mainz in Germany. Her main research interests ordinary and partial differential equations, integral and integro differential-difference equations, dynamical systems and their analysis, numerical methods, mathematical biology and scientific computation.


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DOI: 10.11121/ijocta.2022.1219
Published: 2022-07-29

How to Cite

Gokce, A., & Gurbuz, B. (2022). A numerical scheme for the one-dimensional neural field model. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12(2), 184–193. https://doi.org/10.11121/ijocta.2022.1219



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