The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms

Ramazan Gencay () and W. Davis Dechert
Additional contact information
W. Davis Dechert: University of Houston

Studies in Nonlinear Dynamics & Econometrics, 1996, vol. 1, issue 3, pages 2

Abstract:

The method of reconstructing an n-dimensional system from observations is to form vectors of m consecutive observations, which for m 2n, is generically an embedding. This is Takens's result. The Jacobian methods for Lyapunov exponents utilize a function of m variables to model the data, and the Jacobian matrix is constructed at each point in the orbit of the data. When embedding occurs at dimension m = n, the Lyapunov exponents of the reconstructed dynamics are the Lyapunov exponents of the original dynamics. However, if embedding only occurs for an m > n, then the Jacobian method yields m Lyapunov exponents, only n of which are the Lyapunov exponents of the original system. The problem is that as currently used, the Jacobian method is applied to the full m-dimensional space of the reconstruction, and not just to the n-dimensional manifold that is the image of the embedding map. Our examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system.

Keywords: Lyapunov exponents; embedded dynamics (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations View citations in EconPapers (7) Track citations by RSS feed

Downloads: (external link)
http://www.bepress.com/cgi/viewcontent.cgi?article=1018&context=snde (application/pdf)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:bpj:sndecm:v:1:y:1996:i:3:n:2

Ordering information: This journal article can be ordered from
http://www.degruyter.com/view/j/snde

Access Statistics for this article

More articles in Studies in Nonlinear Dynamics & Econometrics from De Gruyter
Series data maintained by Peter Golla ().