Modeling Morphogenesis with Reaction-Diffusion Equations

This project studies the nonhomogeneous steady-state solutions of the Gray-Scott model, a system of nonlinear partial differential equations that has received attention in the past decade in the context of pattern formation and morphogenesis. Morphogenesis, or ‘birth of shape’, is the biological term for the initial formation of patterns that occur in development as cells begin to differentiate. The model is a two morphogen reactiondiffusion system in which individual molecules display complex self-organization in aggregate.