Figure 1.

Sample reconstructed attractors for data and surrogates of the Hénon map. Panels (a) and (f) are embedded time series data from the x-component of the Hénon system with the addition of 1% and 10% observational noise (respectively). The remaining panels are representative ATS time series. Panels (b), (c), (d) and (e) are surrogates for panel (a), and Panels (g), (h), (i) and (j) are for panel (f). Each surrogate is computed with a different level of transition probability P. In panels (b) and (g), p = 0.2; in panels (c) and (h), p = 0.4; in panels (d) and (i), p = 0.6; and, in panels (e) and (j), p = 0.8. In each case the attractors reconstructed from the surrogates have the same qualitative features as that of the data – with the possible exception of panel (e). The likely reason for this noted exception is the relatively high transition probability (p = 0.8) and the relatively low noise level (1%). Of course, for smaller values of p (i.e. p = 0.1) the similarity is even more striking.