This paper investigates the replication of experiments by Billock and Tsou [PNAS, 2007] using the controllability of neural fields of Amari-type modelling the cortical activity in the primary visual cortex (V1), focusing on a regular funnel pattern localised in the fovea or the peripheral visual field. The aim is to understand and model the visual phenomena observed in these experiments, emphasising their nonlinear nature. The study involves designing sensory inputs simulating the visual stimuli from Billock and Tsou's experiments. The after-images induced by these inputs are then theoretically and numerically studied to determine their capacity to replicate the experimentally observed visual effects. A key aspect of this research is investigating the effects induced by the nonlinear nature of neural responses. In particular, by highlighting the importance of both excitatory and inhibitory neurons in the emergence of certain visual phenomena, this study suggests that an interplay of both types of neuronal activities plays an essential role in visual processes, challenging the assumption that the latter is mainly driven by excitatory activities alone.