This paper focuses on the modeling of experiments conducted by Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490-8495] using an Amari-type neural field that models the average membrane potential of neuronal activity in the primary visual cortex (V1). The study specifically focuses on a regular funnel pattern localized in the fovea or the peripheral visual field. It aims to comprehend and model the visual phenomena induced by this pattern, emphasizing their nonlinear nature. The research involves designing sensory inputs that mimic the visual stimuli from Billock and Tsou's experiments. The cortical outputs induced by these sensory inputs are then theoretically and numerically studied to assess their ability to model the experimentally observed visual effects at the V1 level. A crucial aspect of this study is the exploration of the effects induced by the nonlinear nature of neural responses. By highlighting the significance of excitatory and inhibitory neurons in the emergence of these visual phenomena, the research suggests that an interplay of both types of neuronal activities plays a crucial role in visual processes, challenging the assumption that the latter is primarily driven by excitatory activities alone.