Scientific Results

Power Spectrum and Diffusion of the Amari Neural Field

Year: 2019

Authors: Salasnich L.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, CNISM, Via Marzolo 8, I-35131 Padua, Italy; CNR INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy

Abstract: We study the power spectrum of a space-time dependent neural field which describes the average membrane potential of neurons in a single layer. This neural field is modelled by a dissipative integro-differential equation, the so-called Amari equation. By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an analytical formula for the power spectrum of the neural field. In addition, after proving that for large wavelengths the linearized Amari equation is equivalent to a diffusion equation which admits space-time dependent analytical solutions, we take into account the nonlinearity of the Amari equation. We find that for large wavelengths a weak nonlinearity in the Amari equation gives rise to a reaction-diffusion equation which can be formally derived from a neural action functional by introducing a dual neural field. For some initial conditions, we discuss analytical solutions of this reaction-diffusion equation.

Journal/Review: SYMMETRY-BASEL

Volume: 11 (2)      Pages from: 134-1  to: 134-8

KeyWords: Neural field theory; Amari equation; power spectrum; reaction-diffusion
DOI: 10.3390/sym11020134

Connecting to view paper tab on IsiWeb: Click here

This site uses cookies. If you decide to continue browsing we consider that you accept their use. For more information about cookies and how to delete them please read our Info Policy on cookies use.
Read more