The Dynamics of Biological Models with Optimal Harvesting

  • Sadiq Al-Nassir Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.
Keywords: Global asymptotically stable, discrete-time predator-prey system, optimal harvesting

Abstract

      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.

Published
2021-09-30
How to Cite
Al-Nassir, S. (2021). The Dynamics of Biological Models with Optimal Harvesting. Iraqi Journal of Science, 62(9), 3039-3051. https://doi.org/10.24996/ijs.2021.62.9.19
Section
Mathematics