Optimal Harvesting of a Predator-Prey System with Additional Food for Predator in Fuzzy Environment

The consideration of a predator-prey system that follows the Rosenzweig-MacArthur model is done in this article. The logistic growth of the prey population is taken into account where the predator population is not present. For the prey population, the functional response of the predator is of Holling type-II. A stock of an additional food term is made available to the predator species. The stability of the equilibrium points are analyzed together with the positivity and existence of the solutions. A Lyapunov function that is befitting is established for the study of the global stability of the system. In real life, due to incomplete information, the parameters involved in the system are imprecise in nature. So, the discussion of optimal taxation policy under fuzzy environment is examined to make the model more realistic. We take into consideration a few hypothetical data sets and verify them numerically.