Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square

Abstract

Bifurcation to spatial patterns in a two-dimensional reaction—diffusion medium is considered. The selection of stripes versus spots is shown to depend on the nonlinear terms and cannot be discerned from the linearized model. The absence of quadratic terms leads to stripes but in most common models quadratic terms will lead to spot patterns. Examples that include neural nets and more general pattern formation equations are considered.