PARAMETER DOMAINS FOR SPOTS AND STRIPES IN MECHANICAL MODELS FOR BIOLOGICAL PATTERN-FORMATION

Mechanochemical models for biological pattern formation have been appl ied to the development of a variety of patterning problems, such as fe ather germ primordia and cartilage formation in the vertebrate limb. L inear analysis has been the main technique for assessing the pattern f ormation potential of these models to date. In this paper we carry out a nonlinear analysis and numerical simulations of a generic model in two spatial dimensions. With these methods, we obtain conditions for g enerating specific spatial patterns such as stripes and spots, and div ide the parameter space into domains giving rise to distinct types of pattern. We accomplish our goal through a study of model parameter dom ains by showing how different mechanical forces affect spatial pattern ing.