The point correlation dimension: performance with nonstationary surrogate data and noise.

The dynamics of many biological systems have recently been attributed to low-dimensional chaos instead of high-dimensional noise, as previously though. Because biological data are invariably nonstationary, especially when recorded over a long interval, the conventional measures of low-dimensional chaos (e.g., the correlation dimension algorithms) cannot be applied. A new algorithm, the point correction dimension (PD2i) was developed to deal with this fundamental problem. In this article we describe the details of the algorithm and show that the local mean PD2i will accurately track dimension in nonstationary surrogate data.