Strong resonance bifurcations for a discrete-time prey–predator model

The aim of this paper is to introduce a two-dimensional discrete-time prey–predator, identify its fixed points, as well as investigate one- and two-parameter bifurcations. Numerical normal forms are used in bifurcation analysis. For this model, the Neimark-Sacker, period doubling and strong resonance bifurcations are observed. Based on the critical coefficients, the bifurcation scenarios can be identified. Based on numerical continuation methods, we use the MATLAB package MatContM to verify the analytical results and observe complex dynamics up to 16- iterate.