Power Spectrum and Diffusion of the Amari Neural Field
AbstractWe 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. View Full-Text
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Salasnich, L. Power Spectrum and Diffusion of the Amari Neural Field. Symmetry 2019, 11, 134.
Salasnich L. Power Spectrum and Diffusion of the Amari Neural Field. Symmetry. 2019; 11(2):134.Chicago/Turabian Style
Salasnich, Luca. 2019. "Power Spectrum and Diffusion of the Amari Neural Field." Symmetry 11, no. 2: 134.
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