ANALISIS KESTABILAN MODEL MANGSA PEMANGSA DENGAN MAKANAN TAMBAHAN PADA PEMANGSA MENGGUNAKAN FUNGSI RESPON HOLLING TIPE IV

Abstract

The interaction between the two populations can result in changes to the growth dynamics of the two populations. In prey populations that live in groups, predator populations have difficulty finding food sources. This resulted in a decrease in predator populations and an imbalance between the two populations. An alternative way that can be done when there is a population imbalance is to provide additional food for predators. In this study, we constructed a two-population predator-prey model with a Holling type IV response function and considered additional food for predators. The first study was in the form of a literature review, then constructing the prey-predator model, followed by analysis by determining the equilibrium point and local stability around the equilibrium point. The suitability of the analysis results is displayed in the simulation in the form of a phase portrait. The results of the analysis obtained three equilibrium points, namely the extinction of prey-predator (E_1), extinction of predators (E_2) and the interaction of prey and predators or when prey-predator live together (E_3). At the equilibrium point E_1 is unstable, while at E_2 and E_3 it is asymptotically stable with certain conditions. The numerical simulation results show that there is a double stability at the equilibrium point E_2 and E_3 when the additional food parameter A=1.3. When A=1.2 only the point of extinction of predators is stable (E_2). The two populations side by side are shown in the phase shot when A=1.9. The presence of additional food A affects the dynamics of the growth of the two populations.

Kata Kunci:  Makanan tambahan, Holling tipe IV, kestabilan, bistabil, model mangsa pemangsa.