  To study the interaction between retinal stimulation by redundant geometrical
patterns and the cortical response in the primary visual cortex (V1), we focus
on the MacKay effect (Nature, 1957) and Billock and Tsou's experiments (PNAS,
2007). We use a controllability approach to describe these phenomena starting
from a classical biological model of neuronal field equations with a non-linear
response function. The external input containing a localised control function
is interpreted as a cortical representation of the static visual stimuli used
in these experiments. We prove that while the MacKay effect is essentially a
linear phenomenon (i.e., the nonlinear nature of the activation does not play
any role in its reproduction), the phenomena reported by Billock and Tsou are
wholly nonlinear and depend strongly on the shape of the nonlinearity used to
model the response function.
