Figure 1

Data sets. Upper panel: the $x$ [$L\left(X\right)$, left] and $z$ [$L\left(Z\right)$, right] coordinates of the Lorenz system. Lower panel: heart rate [$P\left(H\right)$, left] and respiration [$P\left(R\right)$, right] signals, in beats per minute and uncalibrated digitization units, respectively. In the subsequent analysis, each variable is normalized to its empirical cumulative distribution.Reuse & Permissions

Figure 2

(a) First embedding cycle profiles for $\tau$ selection from $N$. The thick line indicates the profile for $L\left(X\right)$ and the thin line the profile for $L\left(Z\right)$. A circle indicates the optimal combination of variable and time delay that is selected from this first cycle. The global minima of $N$ corresponds to the onset of dynamic decoupling. (b) The fraction of $F$ as a function of $m$ for the embedding of the bivariate $L\left(X\right)$ and $L\left(Z\right)$ time series. See the text for a more comprehensive description.Reuse & Permissions

Figure 3

(a) First; (b) second; (c) third; and (d) fourth embedding cycle profiles for $\tau$ selection from $N$. Thick lines indicate profiles for $P\left(H\right)$ and thin lines indicate profiles for $P\left(R\right)$. An arrow indicates the optimal combination of variable and time delay selected from each embedding cycle. From the second (b) to the fourth (d) embedding cycles, a peak is visible at previously selected $\tau$ values. (e) The fraction of $F$ as a function of $m$ for the embedding of the bivariate $P\left(H\right)$ and $P\left(R\right)$ time series. See the text for a more comprehensive description.Reuse & Permissions