Linear Stability Analysis of Turing Patterns on Arbitrary Manifolds
Alan Turing’s mathematical model for pattern formation, based on linear instabilities in reaction-diffusion systems, has been widely applied in chemistry, biology and physics. Most of the modelling applications have been implemented on flat two dimensional domains, even though many of the patterns under investigation, including the celebrated application to animal coat patterns, occur on non-Euclidean two dimensional manifolds. In this work we have described an extension of Turing instability analysis to arbitrary manifolds. Our approach is simple to implement and it readily enables exploration of the effect of the geometry on Turing pattern formation in reaction-diffusion systems on arbitrarily shaped and sized domains.