Noise-controlled slow–fast oscillations in predator–prey models with the Beddington functional response

The influence of environmental fluctuations (modeled as a multiplicative dichotomous noise) on predator–prey interaction is studied using a metapopulation model with N prey-subpopulations. Investigating the role that predator interference plays in the dynamics of such trophic systems, the Beddington functional response is considered. In case the growth rates of prey and predator are widely different, we obtain analytic results by a dynamical mean-field approximation. In some regions of the system parameters, variations of noise amplitude or correlation time can cause transitions of the mean field from a globally stable equilibrium to the stable limit cycle as well as in the opposite direction. The conditions for the occurrence of such a phenomenon are found and illustrated by phase diagrams. Implications of the results on the colored-noise-induced extinction of a predator population are also discussed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007