Combine Logistic to Pray and Impacts of Harvesting on Prey-Predator Model

Abstract

The present article argues about a prey-predator model where the two species are harvested autonomously with constant or variable rates that have been well thought-out. According to the theory of logistic growth, the prey population is increasing. The Lotka-Volterra predator-prey model is modified and adapted into this model. The model has reached its equilibrium points, and the dynamical behavior of the suggested system was examined to display the phase portrait. Model simulations are analyzing, bifurcation diagrams are examined, and the behavior of the solutions' locally and globally is examined. The impacts of logistic and harvesting on the steadiness of stability states are inspected. The main purpose of the article is to implement a mathematical investigate of the model, and it can be obtained that the effect of activities in harvesting is more effective on the dynamical behaviour in the current model. At the end, solution curves are plotted by utilizing the Maple program to explore the dynamical behaviour of the model regarding to the time.