Numerical Simulation of Pattern Formation

Abstract

 

In this talk we examine spatio-temporal pattern formation in reaction-diffusion systems. Our main interest is to identify spatial patterns which evolve in practice from unstable homogeneous steady states. We investigate the role that pre-pattern (Turing) theory may play in the growth and development of solid tumours modelled by the systems. In order to connect our numerical scheme more concretely to the tumour growth application, we simulate spatially heterogeneous patterns on the surface of a growing spherical tumour modelled as a moving-boundary value problem.