Abstract
We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d→d+1. When the number of nearest neighbors arising through projection is zero in dimension , the attractor has been unfolded in this dimension. The precise determination of is clouded by ‘‘noise,’’ and we examine the manner in which noise changes the determination of . Our criterion also indicates the error one makes by choosing an embedding dimension smaller than . This knowledge may be useful in the practical analysis of observed time series.
- Received 24 April 1991
DOI:https://doi.org/10.1103/PhysRevA.45.3403
©1992 American Physical Society