We investigate existence of stationary solutions to an aggrega-tion/diffusion system of PDEs, modelling a two species predator-prey interac-tion. In the model this interaction is described by non-local potentials that are mutually proportional by a negative constant −α, with α > 0. Each species is also subject to non-local self-attraction forces together with quadratic diffusion effects. The competition between the aforementioned mechanisms produce a rich asymptotic behavior, namely the formation of steady states that are com-posed of multiple bumps, i.e. sums of Barenblatt-type profiles. The existence of such stationary states, under some conditions on the positions of the bumps and the proportionality constant α, is showed for small diffusion, by using the functional version of the Implicit Function Theorem. We complement our results with some numerical simulations, that suggest a large variety in the possible strategies the two species use in order to interact each other.

Multiple patterns formation for an aggregation/diffusion predator-prey system

Fagioli S.
;
Jaafra Y.
2021

Abstract

We investigate existence of stationary solutions to an aggrega-tion/diffusion system of PDEs, modelling a two species predator-prey interac-tion. In the model this interaction is described by non-local potentials that are mutually proportional by a negative constant −α, with α > 0. Each species is also subject to non-local self-attraction forces together with quadratic diffusion effects. The competition between the aforementioned mechanisms produce a rich asymptotic behavior, namely the formation of steady states that are com-posed of multiple bumps, i.e. sums of Barenblatt-type profiles. The existence of such stationary states, under some conditions on the positions of the bumps and the proportionality constant α, is showed for small diffusion, by using the functional version of the Implicit Function Theorem. We complement our results with some numerical simulations, that suggest a large variety in the possible strategies the two species use in order to interact each other.
File in questo prodotto:
File Dimensione Formato  
1556-1801_2021_3_377.pdf

non disponibili

Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 1.76 MB
Formato Adobe PDF
1.76 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/176238
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact