Non-local competition slows down front acceleration during dispersal evolution - Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes Accéder directement au contenu
Article Dans Une Revue Annales Henri Lebesgue Année : 2022

Non-local competition slows down front acceleration during dispersal evolution

Résumé

We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is non-local with respect to one variable. We prove that the rate of acceleration is slower than the rate of acceleration predicted by the linear problem, that is, without saturation. This hindering phenomenon is the consequence of a subtle interplay between the non-local saturation and the non-trivial dynamics of some particular curves that carry the mass at the front. A careful analysis of these trajectories allows us to identify the value of the rate of acceleration. The article is complemented with numerical simulations that illustrate some behavior of the model that is beyond our analysis.
Fichier principal
Vignette du fichier
slow_toads.pdf (2.32 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01963994 , version 1 (06-10-2022)

Identifiants

Citer

Vincent Calvez, Christopher Henderson, Sepideh Mirrahimi, Olga Turanova, Thierry Dumont. Non-local competition slows down front acceleration during dispersal evolution. Annales Henri Lebesgue, 2022, 5, pp.1-71. ⟨10.5802/ahl.117⟩. ⟨hal-01963994⟩
142 Consultations
27 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More