We investigate degenerate cross-diffusion equations, with a rank-deficient diffusion-matrix, modelling multispecies population dynamics driven by partial pressure gradients. These equations have recently been found to arise in mean-field limit of interacting stochastic particle systems. To date, their analysis multiple space dimensions has confined the purely convective case equal mobility coef...

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...

The population model by Busenberg and Travis is a paradigmatic in ecology tumor modeling because its ability to capture interesting phenomena such as segregation of populations. Its singular mathematical structure enforces the consideration regularized problems deduce properties fundamental existence solutions. In this article we perform weakly nonlinear stability analysis general class study c...

This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore unique positive equilibrium solution the that is globally asymptotically stable. Additionally, we show this remains locally linearly stable, even in presence diffusion. means does not follow classical Turing instability. However, it becomes unstable only when cross-dif...