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Predicting the behavior of a chaotic pendulum with a variable interaction potential
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The behavior of a chaotic physical pendulum is significantly modified through the addition of a magnetic interaction. The extended behavior is studied through identifying distinct characteristics in the Poincaré sections and turning point maps of the systems. The validity of our model is shown through simulated bifurcations generated from coefficients estimated at a number of different frequencies. These simulated bifurcations also demonstrate that coefficients estimated at one frequency can be used to predict the behavior of the system at a different drive frequency. A quantitative measure of the correlation dimension shows that the simulated Poincaré diagrams are in good agreement with experiment and theory. Possible sources of bias in modeled systems are identified.
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