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In this study, we investigate the intricate connection between visualperception and the mathematical modelling of neural activity in the primaryvisual cortex (V1), focusing on replicating the MacKay effect [Mackay, Nature1957]. While bifurcation theory has been a prominent mathematical approach foraddressing issues in neuroscience, especially in describing spontaneous patternformations in V1 due to parameter changes, it faces challenges in scenarioswith localised sensory inputs. This is evident, for instance, in Mackay'spsychophysical experiments, where the redundancy of visual stimuli informationresults in irregular shapes, making bifurcation theory and multi-scale analysisless effective. To address this, we follow a mathematical viewpoint based onthe input-output controllability of an Amari-type neural fields model. Thisframework views the sensory input as a control function, corticalrepresentation via the retino-cortical map of the visual stimulus that capturesthe distinct features of the stimulus, specifically the central redundancy inMacKay's funnel pattern ``MacKay rays''. From a control theory point of view,the exact controllability property of the Amari-type equation is discussed bothfor linear and nonlinear response functions. Then, applied to the MacKay effectreplication, we adjust the parameter representing intra-neuron connectivity toensure that, in the absence of sensory input, cortical activity exponentiallystabilises to the stationary state that we perform quantitative and qualitativestudies to show that it captures all the essential features of the inducedafter-image reported by MacKay

On the mathematical replication of the MacKay effect from redundant stimulation