Morphogenesis: how can periodic patterns be generated from non-linear interactions?

Abstract

The phenomenon of morphogenesis can be explained by a mechanism containing diffusion-driven instabilities, proposed by Alan Turing. Morphogenesis is about the formation of anatomical structures and periodic patterns in living organisms that can be found in nature. Here I focused on the role of diffusion in the emergence of stationary periodic structures from small perturbations of the homogeneous state. Specially, which conditions parameter values must accomplish to drive pattern formation. The investigation is centered on the non-linear interactions in a system of two different chemical species and which significative changes in pattern arising are done if we add a binding substrate to this kind of system, in concrete, how does it change instability conditions. The study is done through analytical and computational methods to find these conditions and to verify them with simulations