Global Analysis of Stage Structure Two Predators Two Prey Systems Under Harvesting Effect for Mature Predators

Abstract

Abstract This article examines set a prey-predator population model system with structural stages. Development of a mathematical model of a sustainable population of a population of living things. Structure stages are formed in predator populations, namely immature and mature. The predation function that corresponds to the characteristics in the ecosystem is the predation process of Holling I. The interaction in the population model that is carried out analysis is the equilibrium value formed from the population model. There are eight equilibrium values that arise from simple simulations. The equilibrium is E 1(0,0,0,0), E 2(0, k,0,0), E 3(k,0,0,0), E 4(k, k,0,0), E 5(0,0,0, A 1), E 6(A 2,0, A 3, A 4), E 7(0, A 5, A 6, A 7) and E 8(A 8, A 9, A 10, A 11). However, only one equilibrium value is analyzed to obtain stability. Stability is seen by requiring four eigenvalues with the Jacobian matrix. As well as the chosen value is used to find the amount of harvest carried out. The linearization of differential equations is an alternative way in this study to obtain equilibrium values. Each equilibrium value has the characteristics and terms of its stability. The Routh-Hurwitz criterion becomes a condition of its stability characteristics. Meanwhile, exploitation efforts in the population are carried out to see the changes that occur. Harvesting carried out obtained harvesting business W = 0.01313666667. For the maximum benefit obtained π = 4.997259008. This advantage is the stability and sustainability of the ecosystem.