DYNAMICAL BEHAVIORS OF A DISCRETE-TIME PREY-PREDATOR MODEL WITH HARVESTING EFFECT ON THE PREDATOR
Zohreh Eskandari, Parvaiz Ahmad Naik, Mehmet Yavuz
Abstract
This study investigates the dynamics of a discrete-time prey-predator model with a harvesting effect on the predator. During the analysis of the bifurcations at the interior fixed point, we find that there are some generic bifurcations, including fold, flip, Neimark-Sacker, and strong resonance bifurcations. Using the normal form theory and the center manifold theorem, we can characterize these bifurcations. Furthermore, we determine the non-degeneracy conditions for the computed bifurcations and compute the critical normal form coefficients. Our analysis of the obtained analytical results as well as the revealing of more complex dynamical behaviors that cannot be achieved analytically is carried out using the numerical continuation method by computing several bifurcation curves emanating from the detected bifurcation points.