Speaker
Description
Many mathematical models describing vegetation patterns are based on biomass–water interactions, due to the impact of this limited resource in arid and semi-arid environments. However, in recent years, a novel biological factor called autotoxicity has proved to play a key role in vegetation spatiotemporal dynamics, particularly by inhibiting biomass growth and increasing its natural mortality rate.
Recent work \cite{GIS25} has shown that it is possible to produce stable close-to-equilibrium patterns using biomass-autotoxicity coupling alone, without water as a model component, using a cross-diffusion model for biomass and toxicity dynamics as the fast-reaction limit of a three-species system involving dichotomy and different time scales.
We study the emergence of multiscale, far-from-equilbrium patterns in the biomass-autotoxicity cross-diffusion model using geometric singular perturbation theory (GSPT). We prove that, when the cross-diffusion term is sufficiently strong, periodic multi-scale patterns can be explicitly constructed, and confirm our theoretical results with numerical simulations. In addition, we show that for weaker cross-diffusion, the family of far-from-equilibrium patterns naturally contains the Turing patterns that were observed in \cite{GIS25}. Our research combines the novel application of GSPT to cross-diffusion systems with the fundamental ecological insight that multiscale vegetation patterns can be produced by biomass-autotoxicity interaction only.
Bibliography
@misc{GIS25,
author = {Giannino, F. and Iuorio, A. and Soresina, C.},
title = {Beyond water limitation in vegetation–autotoxicity patterning:
a cross-diffusion model},
journal = {submitted},
year = {2025},
url = {https://arxiv.org/abs/2506.03981},
doi = {10.48550/arxiv.2506.03981},
publisher = {arXiv}
}
