Patterns in Square Arrays of Coupled Cells

摘要: In recent years it has been observed that reaction]diffusion equations Ž . with Neumann boundary conditions as well other classes of PDEs possess more symmetry than which may be expected, and these ‘‘hidden’’ symmetries affect the generic types bifurcation occur w x see Golubitsky et al. 6 , Field 5 Armbruster Dangelmayr 1 Crawford 2 Gomes Stewart 8, 9 others addition, equilibria highly developed patterns exist for equaw tions might otherwise expected. Epstein 4 show also discretizations on an interval. particular, such systems have well-defined patterns, considered a discrete analog Turing patterns. this paper, we use idea similar to one in same phenomena occurs square satisfying conditions. Such lead n = arrays identically coupled cells. By embedding original array into new 2n array, can embed condition discretization periodic increase group from