Qualitative Analysis of a Nonautonomous Beverton-Holt Ricker Model

We explore a planar discrete-time model from population dynamics subject to a general aperiodic time-varying environment in order to illustrate the recent theory of nonautonomous dynamical systems. Given such a setting, the mathematical standard tools from classical dynamical systems and bifurcation theory cannot be employed, since for instance equilibria typically do not exist or eigenvalues yield no stability information. For this reason, we apply a combination of contemporary analytical and numerical techniques adequate to tackle such situations.