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.

翻译：本文聚焦于使用Amari型神经场对Billock与Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490--8495] 所进行实验的建模研究。该神经场模拟了初级视觉皮层（V1）神经元活动的平均膜电位。研究特别关注位于中央凹或周边视野的规则漏斗状图案，旨在理解并建模由该图案诱导的视觉现象，并强调其非线性本质。本研究设计了模拟Billock与Tsou实验中视觉刺激的感官输入，随后通过理论与数值方法分析这些感官输入诱导的皮层输出，以评估其在V1层面对实验观测视觉效应的建模能力。本研究的核心在于探究神经响应非线性特性所产生的影响。通过揭示兴奋性与抑制性神经元在这些视觉现象产生中的关键作用，研究指出两类神经元活动的相互作用在视觉处理过程中扮演着决定性角色，这对以往认为视觉处理主要由兴奋性活动驱动的假设提出了挑战。