The trajectory intersection: An approach for nonlinear down-sampling

Faezeh Sohrabi and Mohammad Bagher Khodabakhshi

Chaos, Solitons & Fractals, 2019, vol. 124, issue C, 10-17

Abstract: Poincaré section is a method for representing the trajectory of dynamical systems in terms of a set of discrete points in a lower dimension. Herein, inspired by the idea of the Poincaré section, we proposed a method for drastically reducing the size of a data set that describes a dynamical system, principally a dynamical system operating in the chaotic regime, while retaining its essential information. The main idea of the proposed method is finding an optimal plane intersecting the trajectory of the system based on information entropy. First, a novel formulation of the trajectory intersection as a differentiable closed form transformation is proposed. Then, optimal parameters of the intersection plane are found through numerical optimization. Finally, the resulting points are arranged in unique coordination by use of principal component analysis (PCA). Our findings indicate that this method is able to preserve the behavior of dynamical systems in both of the state space and time domain. Moreover, transitions of the system among dynamical regimes are detectable. Therefore, our methodology characterizes the dynamical system adequately while the number of samples is noticeably reduced.

Keywords: Nonlinear time series analysis; Poincaré section; Dynamical systems; Information entropy (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:124:y:2019:i:c:p:10-17

DOI: 10.1016/j.chaos.2019.04.034

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