Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting

Using the forward Euler method, we derive a discrete predator-prey system of Gause type with constant-yield prey harvesting and a monotonically increasing functional response in this paper. First of all, a detailed study for the existence and local stability of fixed points of the system is obtained by invoking an important lemma. Mainly, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the saddle-node bifurcation and the flip bifurcation of this system to occur. Finally, with the use of Matlab software, numerical simulations are carried out to illustrate the theoretical results obtained and reveal some new dynamics of the system-chaos occuring.