Noise-induced ecological shifts in a prey–predator model

This work is devoted to the study of a map that describes the classical model of interaction between two populations of the “predator–prey” type in the presence of environmental noise. We carry out the analysis from several perspectives. First, deterministic bifurcation scenarios for attractors and their basins of attraction are studied. The critical line method is used to describe the occurrence of non-connected basins of attraction. Subsequently, we analyze the stochastic model using semi-analytical methods, namely the stochastic sensitivity function and the confidence domain method. A constructive parametric description of population extinction caused by random noise is given. An estimate of the critical noise intensity for the occurrence of the described phenomena is obtained. Finally, we provide a descriptive analysis of the extinction time series for prey and predator populations. By establishing the existence of a pronounced right-hand tail of the extinction-time density, we demonstrate that a species might avoid extinction over extended time periods.