Pattern Formation in a Generalized Chemotactic Model

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.