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.

翻译：为研究冗余几何模式对视网膜刺激与初级视觉皮层(V1)皮层反应之间的相互作用，我们聚焦于麦凯效应(Nature, 1957)以及Billock与Tsou的实验(PNAS, 2007)。我们采用可控性方法，从包含非线性响应函数的经典神经元场方程生物学模型出发，描述这些现象。包含局部控制函数的外部输入被解释为这些实验中使用的静态视觉刺激的皮层表征。我们证明，尽管麦凯效应本质上是一种线性现象（即激活的非线性特性在其再现过程中不起任何作用），但Billock与Tsou报告的现象则完全是非线性的，且强烈依赖于用于建模响应函数的非线性形状。