Population dynamics of a modified predator-prey model with economic harvesting

The dynamical behaviors of a predator-prey model with commercial harvesting are studied in the present work. The model is developed from the Leslie predator-prey model with harvesting on predator, which is established by differentialalgebra equations. The harvesting is considered from an economic perspective, and the impacts of the harvesting profit on the dynamics of our model are investigated. Firstly, basing on the parameterisation approach of differential-algebra system, the local stability of positive equilibrium point is studied. Further, by treating the harvesting profit as a bifurcation parameter, the Hopf bifurcation occurring at the equilibrium point is analyzed, and we find a qualitative change in the dynamics. Besides, the stability of centre is also considered. Some computer simulations using Matlab software are presented to support the analytical results. Lastly, we relate the results on mathematics and dynamics with the biology, and interpret these results in terms of ecosystem stability and destruction.