Homogeneous observer for a low-dimensional neural fields model of cortical activity

We propose an observer design for a 3-dimensional model of cortical activity dynamics in the visual cortex, under the measurement of the averaged activity. It is based on the construction of an embedding of the system into a triangular 4-dimensional system where the dynamics are not Lipschitzcontinuous but bear Hölder-continuity properties allowing us to implement a sliding mode observer. We discuss stability of the convergence of the observer with respect to relevant perturbations and provide simulations illustrating the method.