Dynamics of 2D Homographic Ricker map

We apply the Holling type-II functional response as a growth function in the classical two-dimensional Ricker map and propose a discrete-time competition model, namely the two-dimensional (2D) Homographic Ricker map. We investigate the non-linear behavior of the proposed model. This includes the boundedness of the solutions, existence, and uniqueness of the coexisting fixed point. We discuss the geometry of the 2D Homographic Ricker map with the help of critical curves and singular points. Further, with the help of the centre manifold theorem and bifurcation theory, we obtain the specific conditions of the existence of the flip bifurcations in the 2D Homographic Ricker map. Finally, we employ numerical simulations to illustrate the stability and the bifurcation analysis of the competing species. � 2023, The Author(s), under exclusive licence to Springer Nature B.V.