Recently, a population model has been analyzed using the framework of Parrondo’s paradox to explain how behavior-switching organisms can achieve long-term survival, despite each behavior individually resulting in extinction. By incorporating environmental noise, the model has been shown to be robust to natural variations. Apart from the role of noise, the apparent ubiquity of quasi-periodicity in nature also motivates a more comprehensive understanding of periodically-coupled models of Parrondo’s paradox. Such models can enable a wider range of applications of the Parrondo effect to biological and social systems. In this paper, we modify the canonical Parrondo’s games to show how the Parrondo effect can still be achieved despite the increased complexity in periodically-noisy environments. Our results suggest the extension of Parrondo’s paradox to real-world phenomena strongly subjected to periodic variations, such as ecological systems experiencing seasonal changes, disease in wildlife and humans, or resource management.

最近，使用帕隆多悖论的框架对种群模型进行了分析，以解释行为转换生物如何实现长期生存，尽管每种行为各自导致灭绝。通过合并环境噪声，该模型已显示出对自然变化的鲁棒性。除了噪声的作用外，自然界中准周期性的普遍存在还激发了人们对Parrondo悖论的周期耦合模型的更全面的理解。这样的模型可以使帕隆多效应在生物和社会系统中得到更广泛的应用。在本文中，我们修改了规范的Parrondo游戏，以显示尽管在周期性嘈杂的环境中复杂性增加，仍然可以实现Parrondo效果。