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 thought. 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 (PD2_i) was developed to deal with this fundamental problem. In this article we describe the details of the algorithm and show that the local mean PD2_i will accurately track dimension in nonstationary surrogate data.