Turing patterns in an open reactor

Steady spatial chemical patterns have been found in model reaction–diffusion systems but have not yet been observed in any laboratory experiments. The reasons for this are discussed and the need for open reactors is stressed. A model open reactor is investigated in order to guide the experimental search for steady patterns. Specifically, Turing bifurcations in this reactor are studied for a simple autocatalytic chemistry (the Gray–Scott model) in order to determine the effects of varying diffusion coefficients, chemical time scales, and residence time. A description of all the steady-state bifurcations from an initially homogeneous state is obtained. The Liapunov–Schmidt reduction is used to determine the stability of the bifurcating solutions and a steady-state continuation technique is used to follow stable and unstable branches of bifurcating solutions.