Bir biyoekonomik diferansiyel cebirsel hasatlı av-avcı modelinin dinamik sistemler yaklaşımı ile incelenmesi

In this work, we offer a differential algebraic population model which describe the dynamics of predator and prey species with Holling Type II functional response and a harvesting of both the prey and the predator populations. Considering the economic factor, a bioeconomic differential algebraic equation is obtained. We show that the above system displays an interior equilibrium point. This equilibrium is stable when the economic profit is negative. However, as the economic profit is increased this equilibrium loses stability. This phenomenon is known as bifurcation. We investigate this bifurcation both from the view point of singularity induced bifurcation as well as Hopf bifurcation. We rigorously prove that a singularity induced bifurcation occurs when the net economic profit is zero. We also study the existence of Hopf bifurcation by means of normal form analysis. Finally we investigate the theoretical findings by means of numerical simulations. We find that our theoretical results match well with the numerical simulations.