Periodic noise-induced framework for history-dependent Parrondo's switching

Abstract

The growing application of Parrondo's paradox as a model in various ecological settings reveals its extensive relevance in biology and nature. To accommodate the apparent ubiquity of periodicity and quasi-periodicity in natural environments, a recent study proposed a capital-dependent Parrondo model coupled with periodic variations. However, the abundance of biological and social systems that exhibit both capital- and history-dependent characteristics necessitate a more general model. Motivated by this need, we first extended the history-dependent variant of Parrondo's paradox to include periodicity. Next, a novel, history-dependent switching strategy is also proposed. We demonstrated that under this new switching strategy, the Parrondo effect can indeed be achieved. Lastly, a new Parrondo model is devised by combining both capital- and history-dependent Parrondo's games. By including both capital and history, the newly formulated model would find extensive applications in biological and ecological contexts, such as organisms that exhibit behavioral diversity.

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