Analysis of a Model for Complex Skin Patterns

A model for complex skin pattern initiation that couples a reaction-diffusion model for the epidermis to a mechanochemical model for the dermis via certain interaction terms is considered. When each of the component models has a range of unstable wavenumbers, the interaction results in a nonlinear superposition of the two patterns generated in the absence of interaction. A nonlinear analysis of the model predicts the solution behaviour in one and two dimensions that is in good agreement with numerical simulations. The interaction can have a significant effect on the patterns that form for all ratios between the linearly unstable wavenumbers of the component models, and a wide range of complex and simple patterns can form depending on this ratio. These patterns are remarkably similar to many of those observed in nature and, to date, have not been able to be generated by a typical reaction-diffusion or mechanochemical theory alone.