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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2022 (2022)

Commun. Math. Biol. Neurosci. 2022 (2022), Article ID 84

Regional optimal control approach for a spatiotemporal prey-predator model

Marouane Karim, Soukaina Ben Rhila, Hamza Boutayeb, Mostafa Rachik

PDF (447.7 KB) https://doi.org/10.28919/cmbn/7597

Abstract

In this paper, we consider a spatiotemporal Prey-Predator system with a diffusion term. Our main objective is to characterize the two optimal controls that minimize the density of prey population also to minimize the density of the predator population to reach the ecological balance in two imposed different regions ω1 and ω2 (it is not excluded that ω1=ω2). For that reason we prove the existence of a pair of control and provide a characterization of optimal control in term of state and adjoint function. Finally, we present numerical simulation to justify our main results and to support the theoretical conclusions.

Published
29 August 2022
Volume
2022 (2022)
License
CC BY 3.0

Copyright © 2022 Marouane Karim, Soukaina Ben Rhila, Hamza Boutayeb, Mostafa Rachik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

M. Karim, S. Ben Rhila, H. Boutayeb, M. Rachik, Regional optimal control approach for a spatiotemporal prey-predator model, Commun. Math. Biol. Neurosci. 2022 (2022), 84. https://doi.org/10.28919/cmbn/7597

BibTeX
@article{Karim2022,
  author  = {Karim, Marouane and Ben Rhila, Soukaina and Boutayeb, Hamza and Rachik, Mostafa},
  title   = {Regional optimal control approach for a spatiotemporal prey-predator model},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2022},
  year    = {2022},
  pages   = {84},
  doi     = {10.28919/cmbn/7597}
}