Singular perturbations approach to the limit cycle and global patterns in a nonlinear diffusion‐reaction problem with autocatalysis and saturation law

A two‐time scales method (singular perturbations) is used to construct the limit cycle and the global nonuniform steady patterns that appear in a diffusion‐reaction process with autocatalysis and the Langmuir–Hinshelwood (Michaelis–Menten, Holling) saturation law. The stability of these nonlinear structures is also established in this paper.