A Comparison Between Four Chaotic Indicators in Systems With Hidden Attractors

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

A nonregular oscillation is not enough to define a system as chaotic. A more in-depth investigation is required to prove the existence of chaotic behavior, which is challenging. Although many scientists use the Lyapunov Characteristic Exponents to detect chaos, it is not the only method. Several scientists have introduced different methods that utilize various properties of dynamical systems. Hidden Attractors may be chaotic or regular. The fact that they have small basins of attraction introduces difficulties in locating and characterizing them. The paper presents four different chaotic indicators based on the evolution of the deviation vectors: the maximal Lyapunov Exponent, the Lyapunov Characteristic Exponents, the Fast Lyapunov Index (FLI), and the Small Alignment Index. It includes their properties and the advantages and disadvantages of each method. Also, it includes the algorithms to calculate them and their implementation in Python. The paper closes with a comparison between the four indices applied to a system with hidden attractors.

Details

Original languageEnglish
Article number011008
Number of pages12
JournalJournal of computational and nonlinear dynamics
Volume20
Issue number1
Publication statusPublished - Jan 2025
Peer-reviewedYes

External IDs

Scopus 105001109817
ORCID /0000-0002-6200-4707/work/196056484

Keywords

Keywords

  • Lyapunov characteristic exponent, chaos, chaotic index, fast Lyapunov index, hidden attractors, smaller alignment index