Stable orientation tuning in the visual cortex

We study the behaviour of the Ben-Yishai hypercolumn model (Ben-Yishai et al., Proc. Natl. Acad. Sci. USA 92 (1995) 3844) under presentation of oriented stimuli, having extended this model by including plastic afferent (LGN to cortex) connections. We find that Hebbian plasticity creates a self-organising map and show that constraining or modifying the standard Hebb rule in a particular way will lead to a contrast-in sensitive tuning width, thus giving an explanation for persistent orientation tuning as observed in the visual cortex. Our analytical results confirm those of simulations done by Von der Malsburg (Kybernetik 14 (1973) 85) and provide a starting point for further analytical treatment of less restricted stimuli.