Example of Turing's instability by equal diffusion.

In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of some kinetic system is destabilized by diffusion. This mechanism is called Turing's instability, which is one of important mechanisms to organize spatiotemporal patterns. In the case of two-component reaction–diffusion systems, the diffusion coefficients should be different for Turing's instability. Conversely, there exist several chemical models that produce the stable patterns even though the diffusion coefficients are equal. These are often referred to as "far-from-equilibrium phenomenon". To study the pattern formation by equal diffusion, this article presents an example of a kinetic system with a asymptotically stable equilibrium, while the corresponding reaction–diffusion system has a family of unstable stationary solutions that is arbitrarily close to the homogeneous stationary solution. [ABSTRACT FROM AUTHOR]