Harvesting effect a Ratio-Dependent Predator-Prey Model

Abstract

The predator-prey model is mathematically ratio-dependent, always showing dynamics rich in singularity findings. Intervention in the model with the predator-prey model of exploitation is carried out by taking into account harvesting. The ratio-dependent form of harvesting predator-prey model is a very important research project in ecological and mathematical theory. In this study, we discuss the dynamics of the ratio-dependent predator-prey model, as well as the forms of exploitation in the harvesting variable. The form of harvesting offered is sustainable harvesting or referred to as bioeconomic theory. The consideration is that the bioeconomic system is able to obtain maximum benefits and at the same time has ecosystem sustainability for a very long period of time. The results of the analysis were carried out without harvesting and with harvesting. Each form of treatment produces two stable local equilibrium points. Harvesting is done only at the equilibrium point that results in maximum population growth, to prevent extinction. In the trajectory analysis, the movement of population growth before and after harvesting is also shown. In the prey population, the movement of population growth is decreasing but towards great stability. Meanwhile, the predator population has decreased significantly, after harvesting. This condition is very possible to occur in an ecosystem that depends on the ratio-dependent.