On the influence of cross-diffusion in pattern formation

In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence two competing species. We provide deeper understanding on conditions required both cross-diffusion and reaction coefficients non-homogeneous exist, by combining detailed linearized analysis with advanced numerical bifurcation methods via continuation software $\mathtt{pde2path}$. report some experiments suggesting that, when is taken into account, there exist positive outside range parameters homogeneous state positive. Furthermore, also analyze case in self-diffusion terms are considered.