A comparison of different indicators of chaos based on the deviation vectors. Application to symplectic mappings

TL;DR

This paper compares various chaos indicators based on deviation vectors to determine their reliability in analyzing symplectic mappings, recommending a specific set of indicators for effective dynamical system analysis.

Contribution

It provides a systematic comparison of multiple chaos indicators and suggests an optimal combination for analyzing mappings' dynamics.

Findings

FLI and RLI are effective for global phase portrait analysis.

MEGNO and SALI are suitable for individual orbit analysis.

A combined package of these indicators reliably describes system dynamics.

Abstract

The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI); the Fast Lyapunov Indicator (FLI); the Dynamical Spectra of stretching numbers (SSN) and the corresponding Spectral Distance (D); and the Relative Lyapunov Indicator (RLI), which is based on the evolution of the difference between two close orbits, have been included. The experiments presented herein allow us to reliably suggest a group of chaos indicators to analyze a general mapping. We show that a package composed of the FLI and the RLI (to analyze the phase portrait globally) and the MEGNO and the SALI (to analyze orbits individually) is good enough to make a description of the systems' dynamics.