Derivation of cross-diffusion models in population dynamics: dichotomy, time-scales, and fast-reaction
In population dynamics, cross-diffusion describes the influence of one species on the diffusion of another. A benchmark problem is the cross-diffusion SKT model, proposed in the context of competing species to account for stable inhomogeneous steady states exhibiting spatial segregation.
Overview
Even though the reaction part does not present the activator-inhibitor structure, the cross-diffusion terms are the key ingredient for the appearance of spatial patterns . From the modelling perspective, cross-diffusion terms naturally appear in the fast-reaction limit of a ''microscopic'' model (in terms of time scales) presenting only standard diffusion and fast-reaction terms, thus incorporating processes occurring on different time scales . In this talk, recent applications of this approach will be presented, e.g., predator-prey and mutualistic interactions, plant dynamics with autotoxicity effects , and epidemiology.
Bisi, M., Bondesan, A., Groppi, M., Soresina, C. (in preparation) A kinetic model for prey-predator dynamics.
Breden, M., Kuehn, C., Soresina, C. (2021). On the influence of cross-diffusion in pattern formation. Journal of Computational Dynamics 8(2):213-240.
Desvillettes, L., Soresina, C. (2019) Non-triangular cross-diffusion systems with predator-prey reaction terms. Ricerche di Matematica 68(1):295-314.
Giannino, F., Iuorio, A., Soresina, C. (in preparation). The effect of auto-toxicity in plant-growth dynamics: a cross-diffusion model.
Kuehn, C., Soresina, C. (2020). Numerical continuation for a fast-reaction system and its cross-diffusion limit. Partial Differential Equations and Applications 1:7.
Presenters
Cinzia Soresina, Montalcini Tenure-Track Assistant Professor, Department of Mathematics, University of Trento, Italy
Brief Biography
Cinzia Soresina is a Montalcini tenure-track assistant professor at the Department of Mathematics at the University of Trento in Italy, working in the Mathematical Biology group led by Prof. Andrea Pugliese. Previously, she was a Marie Curie fellow at the Technical University of Munich in Germany and a university assistant at the University of Graz in Austria. Most of her experience is in applied mathematics: her studies and research focus on mathematical models of population dynamics, dynamical systems, bifurcation analysis, and cross-diffusion.