Nonlinear Correlations/ Interrelations

1. Detection of an El Niño impact on local rainfall in NW Argentina, 30000 years ago
2. Laser experiment with delayed feedback

Example:
Detection of an El Niño impact on local rainfall in NW Argentina, 30000 years ago

  

The Santa Maria Basin in NW Argentina is located between opposite El Niño influences. These influences have changed for the Santa Maria Basin during the Holocene. Varved lake sediments from the Santa Maria Basin offer an archive of variations in the rainfall 30000 years ago.

Cross recurrence plots (CRPs) reveal epochs of a similar dynamics in precipitation (present-day and past) and the El Niño. Here the CRP between the present-day rainfall in Salta and the Southern Oscillation Index (SOI) is shown. From a statistical investigation of the CRPs between modern/past precipitation and El Niño data (SOI) the existence of an El Niño-like impact on the local climate in NW Argentina 30000 years ago can be inferred.

Reference:

Marwan, N., Trauth, M. H., Vuille, M., Kurths, J.: Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods, Climate Dynamics, 21(3-4), 2003, 317-326, doi:10.1007/s00382-003-0335-3, Article (PDF).

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Example: Laser experiment with delayed feedback

An optical feedback experiment. The dynamic of the laser intensity can be described with two coupled differential equations. However, for large delays the dynamics can be described with one equation. The delay components of this equation can be determined by using the ACE algorithm.

The maximal-correlation function (right) exhibits the typical delays in the system more significant than the auto-correlation function (right).

The optimal transformations, which are used for the model. Where the term f₀(y_t) is strong non-linear, the feedback term f₂(y_t) is linear.

Reference:

Voss, H., Kurths, J.: Reconstruction of nonlinear time delay models from data by the use of optimal transformations, Phys. Lett. A, 234, 1997, 336-344, doi:10.1016/S0375-9601(97)00598-7, Article (PDF).

Voss, H., Kolodner, P., Abel, M., Kurths, J.: Amplitude equations from spatiotemporal binary-fluid convection data. Phys. Rev. Lett., 83(17), 1999, 3422-3425, doi:10.1103/PhysRevLett.83.3422, Article (PDF).

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