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). Starting from a classical biological model of neuronal fields equations with a non-linear response function, we use a controllability approach to describe these phenomena. 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:为了研究由冗余几何形态引起的视网膜刺激与原始视觉皮层皮层(V1)的皮层反应之间的相互作用,我们侧重于MacKay效应(自然,1957年)以及Billock和Tsou的实验(PNAS,2007年)。从神经场方程式的经典生物模型和非线性反应功能开始,我们采用可控性方法来描述这些现象。含有本地化控制功能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质表示。我们证明,虽然麦凯效应本质上是一种线性现象(即激活的非线性在繁殖中不发挥任何作用),但博洛克和Tsou所报告的现象完全是非线性现象,并在很大程度上取决于用于模拟反应功能的非线性形状。