Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a clear understanding about all possible types of dynamical regimes in classical reaction-diffusion models, such as Lotka- Volterra competition models with spatial dependence. In this study, we demonstrate some new types of wave propagation and pattern formation in a classical three species cyclic competition model with spatial diffusion, which have been so far missed in the literature. These new patterns are characterized by a high regularity in space, but are different from patterns previously known to exist in reaction-diffusion models, and may have important applications in improving our understanding of biological pattern formation and invasion theory. Finding these new patterns is made technically possible by using an automatic adaptive finite element method driven by a novel a posteriori error estimate which is proved to provide a reliable bound for the error of the numerical method. We demonstrate.

Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework / Cangiani, A.; Georgoulis, E. H.; Morozov, A. Yu.; Sutton, O. J.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - 474:2213(2018), pp. 1-23. [10.1098/rspa.2017.0608]

Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework

Cangiani A.;
2018-01-01

Abstract

Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a clear understanding about all possible types of dynamical regimes in classical reaction-diffusion models, such as Lotka- Volterra competition models with spatial dependence. In this study, we demonstrate some new types of wave propagation and pattern formation in a classical three species cyclic competition model with spatial diffusion, which have been so far missed in the literature. These new patterns are characterized by a high regularity in space, but are different from patterns previously known to exist in reaction-diffusion models, and may have important applications in improving our understanding of biological pattern formation and invasion theory. Finding these new patterns is made technically possible by using an automatic adaptive finite element method driven by a novel a posteriori error estimate which is proved to provide a reliable bound for the error of the numerical method. We demonstrate.
2018
474
2213
1
23
20170608
https://arxiv.org/abs/1709.10043
Cangiani, A.; Georgoulis, E. H.; Morozov, A. Yu.; Sutton, O. J.
File in questo prodotto:
File Dimensione Formato  
CangianiGeorgoulisMorozovSutton-RoyalSocProcA-2018.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 1.75 MB
Formato Adobe PDF
1.75 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: https://hdl.handle.net/20.500.11767/135243
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 14
social impact