Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback - Université Paris 8 Vincennes - Saint-Denis Accéder directement au contenu
Article Dans Une Revue IEEE Control Systems Letters Année : 2017

Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback

Résumé

Several stains of the intracellular parasitic bacterium Wolbachia limit severely the competence of the mosquitoes Aedes aegypti as a vector of dengue fever and possibly other arboviroses. For this reason, the release of mosquitoes infected by this bacterium in natural populations is presently considered a promising tool in the control of these diseases. Following works by M. Turelli [4] and subsequently M. Strugarek et al. [21, 22], we consider a simple scalar reaction-diffusion model describing the evolution of the proportion of infected mosquitoes, sufficient to reveal the bistable nature of the Wolbachia dynamics. A simple distributed feedback law is proposed, whose application on a compact domain during finite time is shown to be sufficient to invade the whole space. The corresponding stabilization result is established for any space dimension.
Fichier principal
Vignette du fichier
control_v2.pdf (484.62 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01480833 , version 1 (01-03-2017)
hal-01480833 , version 2 (08-05-2017)
hal-01480833 , version 3 (09-05-2017)

Identifiants

Citer

Pierre-Alexandre Bliman, Nicolas Vauchelet. Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback. IEEE Control Systems Letters, 2017, 1 (1), pp.62-67. ⟨10.1109/LCSYS.2017.2703303⟩. ⟨hal-01480833v3⟩
985 Consultations
450 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More