Speaker
Description
In this talk we discuss the influence of inertial effects on the formation and evolution of vegetation patterns on sloped arid terrains in different dynamical regimes. Analyses are carried out in a hyperbolic extension of the one-dimensional Klausmeier model [1], where autotoxicity effects are also considered. As the system moves away from the wave bifurcation threshold, two classes of solutions, corresponding to the emergence of qualitatively different coherent structures, arise: small-amplitude periodic migrating bands near onset and large-amplitude travelling pulses in far-from-equilibrium conditions [2].
For the first class of solutions, we address both linear and multiple scale weakly nonlinear analyses [3]. Our results reveal that inertia acts as a destabilising mechanism, reduces the pattern migration speed and may even reverse the dynamical regime, from supercritical to subcritical, thus leading to hysteresis.
For the second class of solutions, we investigate the key qualitative features of travelling vegetation pulses via Geometric Singular Perturbation Theory [4]. In far-from-equilibrium conditions, inertia is shown to increase pulse speed while preserving the intrinsic multiscale structure of the solution, in full agreement with the numerical findings.
Overall, we show that inertia does not exclusively act as a time lag, but it constitutes an additional degree of freedom which should be considered in shaping vegetation dynamics under environmental stress.
Bibliography
@article{1,
title = {Regular and {Irregular} {Patterns} in {Semiarid} {Vegetation}},
volume = {284},
issn = {0036-8075, 1095-9203},
url = {https://www.science.org/doi/10.1126/science.284.5421.1826},
doi = {10.1126/science.284.5421.1826},
language = {en},
number = {5421},
urldate = {2026-05-11},
journal = {Science},
author = {Klausmeier, Christopher A.},
month = jun,
year = {1999},
pages = {1826--1828},
}
@article{2,
title = {How inertia affects autotoxicity-mediated vegetation dynamics: from close-to to far-from-equilibrium patterns},
copyright = {Creative Commons Attribution 4.0 International},
shorttitle = {How inertia affects autotoxicity-mediated vegetation dynamics},
url = {https://arxiv.org/abs/2603.10086},
doi = {10.48550/ARXIV.2603.10086},
urldate = {2026-05-11},
publisher = {arXiv},
author = {Consolo, Giancarlo and Currò, Carmela and Grifò, Gabriele and Iuorio, Annalisa and Valenti, Giovanna and Veerman, Frits},
year = {2026},
keywords = {Pattern Formation and Solitons (nlin.PS), Analysis of PDEs (math.AP), Dynamical Systems (math.DS), FOS: Physical sciences, FOS: Physical sciences, FOS: Mathematics, FOS: Mathematics, 34C37, 35B25, 35B32, 35B35, 35B36, 35C07, 35L40, 92D40},
}
@article{3,
title = {Stationary and {Oscillatory} patterned solutions in three-compartment reaction–diffusion systems: {Theory} and application to dryland ecology},
volume = {186},
issn = {09600779},
shorttitle = {Stationary and {Oscillatory} patterned solutions in three-compartment reaction–diffusion systems},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0960077924008397},
doi = {10.1016/j.chaos.2024.115287},
language = {en},
urldate = {2026-05-11},
journal = {Chaos, Solitons \& Fractals},
author = {Consolo, Giancarlo and Curró, Carmela and Grifó, Gabriele and Valenti, Giovanna},
month = sep,
year = {2024},
pages = {115287},
}
@article{4,
title = {Far-from-{Equilibrium} {Traveling} {Pulses} in {Sloped} {Semiarid} {Environments} {Driven} by {Autotoxicity} {Effects}},
volume = {85},
issn = {0036-1399, 1095-712X},
url = {https://epubs.siam.org/doi/10.1137/24M1669499},
doi = {10.1137/24M1669499},
language = {en},
number = {1},
urldate = {2026-05-11},
journal = {SIAM Journal on Applied Mathematics},
author = {Grifò, Gabriele and Iuorio, Annalisa and Veerman, Frits},
month = feb,
year = {2025},
pages = {188--209},
}
