Switching induced oscillations in discrete one-dimensional systems

In ecological modeling, seasonality can be represented as an alternation between environmental conditions. We consider a switching strategy that alternates between two undesirable dynamics and find that they can yield a desirable periodic behavior in the case of the Beverton-Holt, Ricker, and modified Ricker maps, which have been extensively used to model ecological populations. For the Ricker and modified Ricker models, we observe coexistence of attractors, which, under the same conditions, define basin of attractions, and the final dynamic behavior depends on the initial conditions.