Stability analysis of harvesting in a predator-prey model

The stability properties are studied for a Lotka-Volterra type two-prey-one-predator model where the predator is harvested. Two different harvesting strategies are applied, constant harvest quota and constant harvest effort. The temporal behaviour of the population dynamics for different harvest intensities is investigated, which includes phenomena such as periodic and chaotic oscillations. It is demonstrated that a constant harvest quota on the predator may destabilize a system that is stable when a constant harvest effort is applied. For the studied region of the parameter space, we show that an increased harvest quota leads to an increased stationary abundancy of the predator.