Abstract:
Shigesada, Kawasaki, and Teramoto showed that introducing cross-diffusion effects in the spatial Lotka–Volterra competition
model can destabilise the spatially homogeneous equilibrium and generate spatial patterns. In this seminar, I will present recent work in collaboration with Tommaso Lorenzi and Gaetana Gambino, in which we examined the effect of phenotype heterogeneity in competing populations. In particular, in our modelling framework, phenotype diversity affects movement and interactions between individuals.
Motivated by cellular plasticity, we considered a regime of rapid phenotype switching and derived conditions for cross-diffusion- and phenotype-driven instabilities. Finally, I will present numerical simulations to illustrate the role of the phenotype distribution and its impact on competitive outcomes.

This Seminar is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P.,  under the scope of the projects \href{https://doi.org/10.54499/UID/00297/2025}{\textcolor{blue}{UID/00297/2025}} and \href{https://doi.org/10.54499/UID/PRR/00297/2025}{\textcolor{blue}{UID/PRR/00297/2025}} (Center for Mathematics and Applications