Turing Instability in Small Arrays

We systematically survey the Turing threshold conditions and the structural mode that becomes unstable, for arrays of two, three, and four coupled reactors with Lengyel-Epstein kinetics. The results illustrate the importance of the value of the coupling strength on the occurrence of a Turing instability. They also provide the 

For two coupled reactors, the Laplacian matrix of the graph Q reads 

There is only one nonuniform structural mode, and we obtain the Turing threshold 

The mass-transfer coefficient k must lie in the interval (0, k ), see above, for Turing patterns to occur, where 

A strict upper bound for k is given by /Cgup = 3/2, the limit of k, 

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