Seasonality and the logistic map

Nonlinear difference equations, such as the logistic map, have been used to study chaos and also to model population dynamics. Here we propose a model that extends the “lose + lose = win” behavior found in Parrondo's Paradox, where switching between chaotic parameters in the logistic map yields periodic behavior (“chaos + chaos = order”). The model uses twelve parameters each reflecting the conditions of one of the twelve months. In this paper we study the effects of smooth-transitioning parameters and the robust system that emerges.