Stability and further analytical bifurcation behaviors of Moran-Ricker model with delayed density dependent birth rate regulation (Q2423598)

A Moran-Ricker model with delayed density dependent birth rate is considered. Some numerical bifurcation tools are used to understand how different intensities of delay factors, due to previous generations, lead to significantly high complexities of the dynamical behavior. In order to explain the complicated structural characteristics of this model a novel and effective technique for investigating the analytical bifurcations of three-dimensional discrete models is used. First, a local stability analysis of the fixed points is considered. Then, normal forms theory and perturbation methods are applied to investigate different types of bifurcations. The author proves the existence of transcritical, flip and Neimark-Sacker bifurcations. In addition, it is showed that the model has a chaotic behavior in the sense of Marotto. Finally, numerical simulations are provided to verify the analytic results.