Switching induced oscillations in the logistic map

In ecological modeling, seasonality can be represented as a switching between different environmental conditions. This switching strategy can be related to the so-called Parrondian games, where the alternation of two losing games yield a winning game. Hence we can consider two dynamics that, by themselves, yield undesirable behaviors, but when alternated yield a desirable oscillatory behavior. In this case, we also consider a noisy switching strategy and find that the desirable oscillatory behavior prevails.