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Nonlinear dynamics--or chaos theory, as it is commonly called--has been studied for more than a century. But as Stark and Hardy explain in their Perspective, chaos has only recently become useful in applications such as microwave ovens, production lines, and biomedicine. The authors chart the history of nonlinear dynamics from the 1960s and argue that the recent progress with practical problems is due to a sea change in the field that led to a synergy between hypothesis-driven and data-driven approaches.
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Stark et al. (2003) studied this question.
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