Seasonality as a Parrondian game

Switching strategies can be related to the so-called Parrondian games, where the alternation of two losing games yields a winning game. We consider two dynamics that by themselves yield undesirable behaviors, but when alternated, yield a desirable oscillatory behavior. In the analysis of the alternate-logistic map, we prove that alternating parameter values yielding extinction with parameter values associated with chaotic dynamics results in periodic trajectories. Ultimately, we consider a four season logistic model with either migration or immigration.

► We consider the logistic map as a population model and include parameter switching.
► From bifurcation diagrams, we find parameters that follow the Parrondian Paradox.
► We study a four-season Parrondian model that includes migration or immigration.