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Journal Articles IEEE Control Systems Letters Year : 2017

Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback

Abstract

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.
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Dates and versions

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

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Cite

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⟩
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