ANALYSIS DINAMIC AND BIOECONOMIC OF A PREDATOR-PREY SYSTEM WITH MARINE NATIONAL PARK - Pratama, Rian Ade; Wahyudi, Candra Agus (Universitas Muhammadiyah Ponorogo, 2023)
In the study of fisheries or marine products in developing countries, the problem of managing marine resources is often faced. Excessive exploitation due to weak legal and supervisory sectors is the most frequently used factor. This research involves a predator-prey mathematical model and provides an intervention variable exploitation, namely harvest. Harvest is carried out on two types of species that inhabit two protected areas of the marine national park zone. One of the objectives of the exploitation variable is to provide benefits for harvesters, such as fishermen. Boundary areas in the marine national park zone and points of equilibrium are assigned to research wetting. Stability analysis using the Routh-Hurwitz criteria indicates the survival of the population. The predator-prey model formed resulted in seven non-negative equilibria, but only one equilibrium point met the research assumptions. Numerical simulations are also provided in trajectories from the initial model formation to the bionomic shape. The basic assumption is that harvesting is carried out in the marine national park zone harvesting is carried out only in a limited way. In the prey one population, more can be harvested in the region than the prey two population. Ecologically, the population of prey one lives in a larger carrying capacity area. In the predator-prey model system, the predator-prey model makes it possible to harvest populations that live in a wider area. The wider the area of the marine national park zone, the more it is permitted to carry out exploitation efforts, provided that it is still limited.