View source for Reaction-diffusion system

A '''reaction-diffusion system''' is a mathematical model describing how the concentration of one or more substances evolves under the combined influence of local chemical reactions and spatial diffusion. The canonical form is a set of coupled partial differential equations: $\partial_t u = D \nabla^2 u + f(u)$, where $ is a diffusion matrix and $ encodes the reaction kinetics. These systems are the primary mechanism of spontaneous [[pattern formation]] in homogeneous media.

[[Alan Turing]]'s 1952 paper established that the interplay of a slowly diffusing activator and a rapidly diffusing inhibitor can destabilize a uniform state and generate stable patterns — stripes, spots, and labyrinths — from noise. This [[activator-inhibitor]] mechanism is the mathematical basis of [[morphogenetic field|morphogenetic fields]] and explains patterning in developmental biology, ecology, and chemical systems such as the [[Belousov-Zhabotinsky reaction]]. Reaction-diffusion systems are also a paradigm of [[symmetry breaking]]: the homogeneous state possesses full spatial symmetry, while the patterned solutions do not.

[[Category:Systems]]
[[Category:Mathematics]]
[[Category:Biology]]