Reaction–diffusion system

Summary

A reaction–diffusion system is a system of parabolic equations $\partial_t u = D \Delta u + R(u)$ for several quantities. Each quantity diffuses in space and reacts with the others at each point. It models chemical reactions, population dynamics, the spread of epidemics and the formation of patterns in biology. Depending on the reaction term, solutions can show travelling fronts, spatial patterns or oscillations. Turing showed that diffusion can make a stable uniform state unstable and so create patterns.