Efek Perlindungan Mangsa dan Daya Dukung Variabel pada Sistem Mangsa-Pemangsa dengan Fungsi Respon Beddington-DeAngelis

Abstract

Several species in the world have experienced extinction. To save species from extinction, a system needs to be formulated, one of which is protecting prey. Changes in physical and biological processes also have a role in the environment, namely resulting in dynamically changing carrying capacity. The rate of prey consumption by the average predator, i.e. the response function is also important in the system formulation. In this study, a prey-predator system was constructed with a Beddington-DeAngelis response function that considers prey protection and variable carrying capacity as well as a predation process that takes into account the predator population. In this research, the equilibrium point for prey-predator extinction, predator extinction, and coexistence was determined and then continued to analyze its stability. With a large prey protection value, the predator extinction equilibrium point is asymptotically stable and the coexistence equilibrium point is asymptotically stable, if and only if within a certain range of prey protection parameter values. In addition, simulations were carried out and it was concluded that at certain prey protection values, changes occurred in the stability of the system which depended on the limits of its carrying capacity.