A computable realization of Ruelle's formula for linear response of statistics in chaotic systems

2020/02/10 by Chandramoorthy, Nisha, Wang, Qiqi · 1 citation
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2002.04117

Abstract

We present a computable reformulation of Ruelle's linear response formula for chaotic systems. The new formula, called Space-Split Sensitivity or S3, achieves an error convergence of the order \cal O(1/√(N)) using N phase points. The reformulation is based on splitting the overall sensitivity into that to stable and unstable components of the perturbation. The unstable contribution to the sensitivity is regularized using ergodic properties and the hyperbolic structure of the dynamics. Numerical examples of uniformly hyperbolic attractors are used to validate the S3 formula against a naïve finite-difference calculation; sensitivities match closely, with far fewer sample points required by S3.

Cited by

• A General Framework for Linking Free and Forced Fluctuations via Koopmanism

Related

• Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds
• Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension
• Approximating linear response of physical chaos
• On convergence of linear response formulae in some piecewise hyperbolic maps
• Toward computing sensitivities of average quantities in turbulent flows