Ergodic sensitivity analysis of one-dimensional chaotic maps

•A brief review of numerical methods for sensitivity analysis of chaos is provided.•The space-split sensitivity (S3) method is numerically investigated using 1D chaotic maps.•The derivative of SRB density function is studied intuitively using 1D chaotic examples.•Computational advantage of S3 over t...

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Bibliographic Details
Published in:Theoretical and applied mechanics letters 2020-11, Vol.10 (6), p.438-447
Main Authors: Śliwiak, Adam A., Chandramoorthy, Nisha, Wang, Qiqi
Format: Article
Language:English
Subjects:
Chaotic systems
Ergodicity
Sensitivity analysis
Space-split sensitivity (S3) method
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Summary:•A brief review of numerical methods for sensitivity analysis of chaos is provided.•The space-split sensitivity (S3) method is numerically investigated using 1D chaotic maps.•The derivative of SRB density function is studied intuitively using 1D chaotic examples.•Computational advantage of S3 over the finite difference method is demonstrated. Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic, chaotic systems, rigorously based on the theory of hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps, revealing its computational advantage over naïve finite difference computations of the same statistical response. In addition, we provide an intuitive explanation of the key components of the S3 algorithm, including the density gradient function.
ISSN:2095-0349
DOI:10.1016/j.taml.2020.01.058