Unifying Lyapunov exponents with probabilistic uncertainty quantification

TL;DR

This paper unifies Lyapunov exponents with probabilistic uncertainty quantification to analyze chaos and uncertainty in stochastic dynamical systems with uncertain initial conditions and dynamics.

Contribution

It introduces a framework that combines Lyapunov exponents with stochastic sensitivity for finite-time uncertainty quantification in uncertain dynamical systems.

Findings

Unified Lyapunov and probabilistic uncertainty framework

Applicable to systems with uncertain initial conditions and dynamics

Enhances understanding of chaos and uncertainty in complex systems

Abstract

The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with stochastic sensitivity (which quantifies the uncertainty of an evolving uncertain system whose initial condition is certain) within a finite time uncertainty quantification framework in which both the dynamics and the initial condition of a continuously evolving $ n $-dimensional state variable are uncertain.