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  4. Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model

Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model

MMC.
2022;
Volume 9, Number 3
: pp. 647–662
https://doi.org/10.23939/mmc2022.03.647
Received: April 29, 2022
Revised: July 02, 2022
Accepted: July 05, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 647–662 (2022)

Authors:
  1. Y. Baala
  2. I. Agmour
  3. M. Rachik
1
Analysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, Morocco
2
Analysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, Morocco
3
Analysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, Morocco

In this paper, we propose a new model of spatio-temporal dynamics concerning the tritrophic reaction-diffusion system by introducing Phytoplankton and Zooplankton.  We recall that the phytoplankton and zooplankton species are the basis of the marine food chain.  There is prey in each marine tritrophic system.  The main objective of this work is to control this species's biomass to ensure the system's sustainability.  To achieve this, we determine an optimal control that minimizes the biomass of super predators. In this paper, we study the existence and stability of the interior equilibrium point.  Then, we move to give the characterization of optimal control.

spatio-temporal dynamics
reaction-diffusion system
optimal control
maximizing
stability

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