Index of content:
Volume 26, Issue 12, December 2016
- REGULAR ARTICLES
26(2016); http://dx.doi.org/10.1063/1.4968852View Description Hide Description
We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.
26(2016); http://dx.doi.org/10.1063/1.4970322View Description Hide Description
Noise contamination in experimental data with underlying chaotic dynamics is one of the significant problems limiting the application of many nonlinear time series analysis methods. Although numerous studies have been devoted to the investigation of different aspects of noise—nonlinear dynamics interactions, the effects produced by noise on chaotic dynamics are not fully understood. This study sought to analyze the local effects produced by noise on chaotic dynamics with a smooth attractor. Local Wayland test translation errors were calculated for noise-induced Lorenz and Rössler chaotic models, and for experimental green light photoplethysmogram data. Results demonstrated that under noise induction, local regions on the chaotic attractor with high values of local translation error can be observed. This phenomenon was defined as the local noise sensitivity. It was found that for both models, local noise-sensitive regions were located close to the system's equilibrium points. Additionally, it was found that the reconstructed dynamics represent well the local noise sensitivity of the original dynamics. The concept of local noise sensitivity is expected to contribute to various applied studies, as it reveals regions of chaotic attractors that are sensitive to the presence of noise.