Ergodic Sensitivity Analysis of One-Dimensional Chaotic Maps
arXiv:2007.15594 · doi:10.1016/j.taml.2020.01.058
Abstract
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 naive 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.
arXiv comment20 pages, 17 figures
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Cited by in corpus (4)
- Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems
- An ergodic averaging method to differentiate covariant Lyapunov vectors
- A trajectory-driven algorithm for differentiating SRB measures on unstable manifolds
- Differentiating densities on smooth manifolds