FAYE , Grégory

The aim of this Thesis is to give a deeper understanding of pattern formation in neural field equations with symmetry, and to understand the significance of these symmetries in modeling the visual cortex. Neural field equations are mesoscopic models that describe the spatio-temporal activity of populations of neurons. They were introduced in...

We present a reduction method to study localized solutions of an integrodifferential equation defined on the Poincaré disk. This equation arises in a problem of texture perception modeling in the visual cortex. We first derive a partial differential equation which is equivalent to the initial integrodifferential equation and then deduce that...

In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integrodifferential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we...