Model Lotka-Volterra yang Mempertimbangkan Efek Ketakutan pada Prey dengan Fungsi Respon Holling Tipe II

Abstract

The predator-prey interaction in the paddy field ecosystem between the owl (Tyto alba) and the field rat (Rattus argentiventer) is represented as a predator-prey model that takes the effect of fear into account. The interaction of these two populations uses a type II Holling response function. This predator-prey model is constructed based on the assumption of prey behavior, namely field mice which have a fear effect on owl predators. Based on several reference journals that were developed with a predation pattern using the type II Holling response function. Calculation analysis in this study was carried out by finding the equilibrium point and stability analysis. The results of the analysis show that the equilibrium point ?0 = (0,0), ?1 = (??,0), ?2 = (μm?−μ,−?+√?2−4??2?) and ?3 = (μm?−μ,−?−√?2−4??2?) with A =???2−2???μ+??μ2 > 0, B =???2μ?+??2−2??μ+?μ2, C =?2?μ?−??2?+?μ??. The results of the stability analysis at the equilibrium point show that E0 = (0,0) unstable, E1 = (??,0) is stable provided ?>μ?(?+??) means that prey populations exist and predator populations become extinct when the conversion of prey biomass to predators is greater than intra-prey competition, the points ?2 dan ?3 is stable provided g > μ means that the prey and predator populations remain when the conversion of prey biomass to predators is greater than the natural death of predators. Numerical simulations were carried out to determine the suitability of the results of the analysis using the Pyton application. The results of numerical simulations of the system solution show that the conversion of prey to predator biomass with the parameter g affects the stability of both populations. Keywords: Lotka-Volterra, effect of fear, Holling II. PENDAHULUAN Interaksi makhluk hidup yang terjadi pada ekosistem alam dapat saling mempengaruhi dan memberi efek satu sama lain. Saat berinteraksi, terdapat