Quantifying Chaos: A tale of two maps
Chaotic Dynamics
2012-07-20 v1 Data Analysis, Statistics and Probability
Abstract
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov exponents should demonstrate evidence of convergence; but literature abounds in which this evidence lacks. This paper presents two maps through which it highlights the importance of providing evidence of convergence of Lyapunov exponent estimates. The results suggest cautious conclusions when confronted with real data. Moreover, the maps are interesting in their own right.
Keywords
Cite
@article{arxiv.1207.4659,
title = {Quantifying Chaos: A tale of two maps},
author = {Reason L. Machete},
journal= {arXiv preprint arXiv:1207.4659},
year = {2012}
}
Comments
12 pages, 6 figure. Accepted for publication in Physics Letters A