Abstract

Co-Authors:  Wakil Sarfaraz, Raquel Barreira, Anotida Madzvamuse In this talk, we present analysis of reaction-diffusion systems to understand the role of geometry and linear cross-diffusion. By deriving conditions on the domain length for rectangular, circular and annular geometries, we generate parameter spaces associated with Turing difusion-driven instability, Hopf and trascritical instabilities. Furthermore, by selecting model parameters from the parameter spaces generated under appropriate geometry and linear cross-diffusion, we are able to demonstrate that linear cross-diffusion coupled with appropriate geometry is able to generate patterns which cannot be obtained through the classical long-range inhibition, and short-range activation mechanism for pattern formation. To support theoretical findings, finite element numerical simulations on rectangular, circular and annular geometries are presented.