Resolving statistical uncertainty in correlation dimension estimation

Borovkova, Svetlana; Rosa, Rodolfo; Sardonini, Laura

doi:10.1063/1.3592799

Cited by 2 publications

(2 citation statements)

References 48 publications

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“…Furthermore, we recommend that future studies follow the statistical approach to estimating correlation dimension outlined by Borovkova et al and include our extension into phase space when applicable. 26 …”

Section: Discussionmentioning

confidence: 99%

“…A histogram of the results from the 100 subsets displayed a Gaussian distribution, and the dimension and uncertainty of each simulated phase slice were determined from the mean and standard deviation. This method of calculating correlation dimension is a modification of the method presented by Borovkova et al 26 Due to the size of our data sets, we did not need to apply the parametric bootstrapping technique but rather statistically sampled the dimension in both time and phase space.…”

Section: -mentioning

confidence: 99%

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Predicting the behavior of a chaotic pendulum with a variable interaction potential

Tran

Brost

Johnston

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 Poincar e 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 Poincar e diagrams are in good agreement with experiment and theory. Possible sources of bias in modeled systems are identified. Although it has been the subject of many papers, books, and commercial experimental systems, the ubiquitous physical pendulum still has untapped physics. By taking advantage of magnetic dipoles, we developed a chaotic pendulum that tests our ability to model a system over a broad range of driving conditions with different interaction potentials. Notably, we find the presence of two very different attractors in our system depending on how the system is driven. This differentiates its behavior from other pendulums where the attractor is either wrapped or unwrapped depending on the drive mechanism. We introduce turning point maps that track regions of net torque, as well as Poincar e sections to help visualize the attractors due to the different interaction potentials. Comparisons between bifurcation diagrams and correlation dimension measurements indicate that large scale system behavior encompassing different attractors can be predicted using a single region of chaotic response. In particular, we show that determining correlation dimension values from a single phase slice could introduce bias and that using fitting parameters from a single frequency in simulations may underestimate the uncertainty in the model.

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Section: Discussionmentioning

confidence: 99%

Section: -mentioning

confidence: 99%

Predicting the behavior of a chaotic pendulum with a variable interaction potential

Tran

Brost

Johnston

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

Chaos and periodicities in a climatic time series of the Iberian Margin

Rojo-Garibaldi

Salas‐de‐León

Monreal‐Gómez

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We analyze the time series of the temperature of the sedimentary core MD01-2443 originating from the Iberian Margin with a duration of 420 kyr. The series has been tested for unit-root and a long term trend is estimated. We identify four significant periodicities together with a low climatic activity every 100 kyr, and these were associated with internal and external forcings. Also, we identify a high-frequency fast component that acts on top of a nonlinear, irreversible slow-changing dynamics. We find the presence of chaos in the climate of the Iberian Margin by means of a neural network asymptotic test on the largest Lyapunov exponent. The analysis suggests that the chaotic dynamics is associated with the fast high-frequency component. We also carry out a statistical analysis of the dimensionality of the attractor. Our results confirm the possibility that periodic behavior and chaos may coexist on different time scales. This could lead to different degrees of predictability in the climate system according to the characteristic time scales and/or phase-space locations.

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Resolving statistical uncertainty in correlation dimension estimation

Cited by 2 publications

References 48 publications

Predicting the behavior of a chaotic pendulum with a variable interaction potential

Predicting the behavior of a chaotic pendulum with a variable interaction potential

Chaos and periodicities in a climatic time series of the Iberian Margin

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