Open AccessGlobal Analysis of Stage Structure Two Predators Two Prey Systems Under Harvesting Effect for Mature Predators
Author(s) -
Rian Ade Pratama,
Maria F. V. Ruslau,
- Nurhayati
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1899/1/012099
Subject(s) - population , predation , mathematics , stability (learning theory) , jacobian matrix and determinant , eigenvalues and eigenvectors , linearization , floquet theory , equilibrium point , predator , mathematical economics , control theory (sociology) , differential equation , ecology , statistics , mathematical analysis , economics , biology , physics , computer science , nonlinear system , demography , control (management) , management , quantum mechanics , machine learning , sociology
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 = 0.013137. For the maximum benefit obtained π = 4.997259008. This advantage is the stability and sustainability of the ecosystem.