Patterns in square arrays of coupled cells
The authors investigate discretizations of reaction-diffusion equations in a square lattice. This can be viewed as a system of oscillators which are coupled identical in all directions. Embedding the \(n\times n\)-square into a \(2n\times 2n\)-square enables the treatment of periodic boundary conditions and the investigation of hidden symmetries. The bifurcations of the symmetric steady state solutions of the ordinary differential equations are investigated with the help of the equivariant branching lemma by Vanderbauwhede. Several figures illustrate the various types of symmetric solutions nicely. Finally, stability is investigated and the Brusselator is considered as an example.
scientific article; zbMATH DE number 1031585