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Many patterning events in multi-cellular organisms rely on cell-to-cellcontact signaling, such as the Notch pathway in metazoans. A particularlyinteresting phenomenon in this form of communication is lateral inhibitionwhere a cell that adopts a particular fate inhibits its immediate neighborsfrom doing the same. Dynamical models are of great interest for understandingthe circuit topologies involved in lateral inhibition and for predicting theassociated patterns. Several simplified models have been employed for Notchsignalling pathways in the literature. The objective of this paper is topresent an abstract dynamical model that captures the essential features oflateral inhibition and to demonstrate with dynamical systems techniques thatthese features indeed lead to patterning.

A Broad Dynamical Model for Pattern Formation by Lateral Inhibition