Open AccessThe Dynamics of Biological Models with Optimal Harvesting
Author(s) -
Sadiq Al-Nassir
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.9.19
Subject(s) - pontryagin's minimum principle , maximum principle , mathematics , optimal control , equilibrium point , stability (learning theory) , mathematical optimization , stability theory , point (geometry) , control theory (sociology) , computer science , control (management) , mathematical analysis , differential equation , physics , geometry , nonlinear system , quantum mechanics , machine learning , artificial intelligence
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. We also propose and analyze a prey-predator model with a suggested function growth in prey species. Firstly the existence and local stability of all its equilibria are studied. After that the model is extended to an optimal control problem to obtain an optimal harvesting strategy. The discrete time version of Pontryagin's maximum principle is applied to solve the optimality problem. The characterization of the optimal harvesting variable and the adjoint variables are derived. Finally these theoretical results are demonstrated with numerical simulations.