DAMPAK KEKERINGAN TERHADAP KESTABILAN SISTEM MANGSA PEMANGSA DENGAN FUNGSI RESPON HOLLING TIPE III DAN HASIL PEMANENAN KONSTAN PADA MANGSA

Abstract

ABSTRACT: The dynamic relationship between prey populations and predator populations can be represent in the mathematical model. This research was developed from the mathematical model of predator-prey which was first introduced by Lotka-Volterra, namely by increasing the realism of the model through apply the logistic model to the prey and involving Holling type-III response function. The effects of drought on both populations and constant harvesting of prey are also included in the mathematical model. After the mathematical model is formed, a nondimensional model is then carried out to create a shape from the model that was built previously. This study aims to analyze the impact of drought on the prey-prey system with a type III Holling functional response and constant-yield prey harvesting. There is at least one equilibrium point and there are at most three equilibrium points in the model. Numerical simulations are carried out on the model to see the phase portrait. The simulation results show that if the rate of drought is greater than the intrinsic growth rate of prey then both populations will go towards extinction. However, on the other hand, if the intrinsic growth rate of the prey is greater than the rate of drought, then the dynamics relationship between the predator and prey populations depends on the pattern of constant-yield prey harvesting. Thus, a stable dynamic relationship occurs on the constant-yield prey harvesting at the interval 0<h<=K(r-a1)2