Perilaku Dinamis Model Mangsa-Pemangsa Tipe Gause yang Diperumum dengan Waktu Tunda Pemanenan Konstan

Abstract

There are several mathematical models to describe prey-predator events. One model that has many applications is the generalized Gause type prey-predator model by considering a time delay and a constant harvesting parameter in both prey-predator populations. We performed stability analysis to both models without time delay and with time delay. For the model without time delay, we obtained three equilibrium points with one is spiral stable, while model with time delay possesses equilibrium points which can be either spiral stable or spiral unstable. In addition to the model with time delay, when the value of time delay increases, this causes the appearance of a limit-cycle and supercritical Hopf bifurcation occurs when the equilibrium stability change from spiral stable to spiral unstable.