A New Principle for Controlling the “Butterfly Effect”

Takemasa Miyoshi (Team Principal, Data Assimilation Research Team, RIKEN Center for Computational Science (R-CCS) / Team Director, Prediction Science Research Team, Division of Applied Mathematical Science, RIKEN iTHEMS), has developed a new mathematical framework for efficiently controlling chaos by turning the fundamental limitation of predictability in deterministic chaos—widely known as the “butterfly effect”—to an advantage.

He proposed a “duality principle,” demonstrating that data assimilation, which forms the foundation of weather forecasting (a process that synchronizes a model with the behavior of nature using observational data), and the control of chaos are mathematically twin concepts. Rather than suppressing chaos itself, this new approach exploits the high sensitivity characteristic of chaotic systems to synchronize real-world behavior with a manageable “target trajectory” through only a small amount of “intervention.” In this way, the study theoretically outlines a path toward controlling chaos beyond the conventional limits of predictability.

This achievement provides a theoretical basis for future research in disaster prevention and mitigation—for example, applying minimal interventions to synchronize real atmospheric phenomena with a “typhoon scenario that causes no damage” (a target trajectory) simulated in a model, with the aim of avoiding extreme weather events. It is also expected to have applications in a wide range of fields that exhibit chaotic behavior, including ecosystems and economics.

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