## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Evaluated Signal**} & \multicolumn{2}{c}{**Averaged \(K_{m}\)**} & \multicolumn{2}{c}{**Averaged \(K_{m}\)**} & \multicolumn{2}{c}{**\(K_{m}\) Trend**} \\  & **(600,000 Points)** & & **(150,000 Points)** & **(up to 60,000 Points )** \\ \cline{2-6}  & \(K_{m}\) & \(\sigma\) & \(K_{m}\) & \(\sigma\) & \(K_{m}\) \\ \hline subject number 1 (PPG1) & 0.1318 & \(\pm\)0.0724 & 0.3330 & \(\pm\)0.0410 & 0.1697 \\ \hline subject number 2 (PPG2) & 0.2426 & \(\pm\)0.1946 & 0.3705 & \(\pm\)0.0502 & 0.8959 \\ \hline subject number 3 (PPG3) & 0.1784 & \(\pm\)0.0865 & 0.1619 & \(\pm\)0.0236 & 0.1548 \\ \hline subject number 4 (PPG4) & 0.1268 & \(\pm\)0.0613 & 0.2602 & \(\pm\)0.0274 & 0.1953 \\ \hline subject number 5 (PPG5) & 0.1464 & \(\pm\)0.0969 & 0.2798 & \(\pm\)0.0261 & 0.2873 \\ \hline \end{tabular}
\end{table} 
Table 2: Averaged \(K_{m}\) over 600,000 points (40 min) [**computation time per signal** in a server cluster consisting of 10 computing nodes, with a total of 64 cores and Intel Xeon architecture, and 166 GB of memory: **37 h 18 min** and **11 s**], over 150,000 points (10 min at a half-way point in between the beginning and the completion of the experimental session) in windows of 30,000 points with an overlapping of 50% and the \(K_{m}\) trend from a block size of 5000 points to a block size of 60,000 points in increments of 5000 points (4 min at a half-way point in between the beginning and the completion of the experimental session), of the PPG signals, acquired from five individuals chosen at random. Another relevant result of this work is that as the timescale increases, other factors involved in cardiac rhythm modulation come into play, resulting in a more complex dynamic to subtly enable greater versatility in the cardiac response and, by extension, in the available blood volume at a peripheral level. This more complex dynamic could be chaotic or a preceding behavior, as a transition from a quasi-periodically forced dynamic to a chaotic dynamic via a strange nonchaotic attractor (SNA) [49; 50; 51; 52]. Figure 3: The parameter \(K_{m}\) trend for several reference signals, as well as for PPG signals, acquired from five individuals chosen at random [**computation time per signal** in a server cluster consisting of 10 computing nodes, with a total of 64 cores and Intel Xeon architecture, and 166 GB of memory: **17 h 7 min** and **7 s**]. (**a**) \(K_{m}\) trend for two periodic signals, one quasi-periodic signal, one aperiodic signal, one chaotic signal, and a random signal; as shown in the figure, only the aperiodic signal displays a notable increasing trend as more points are added in the computation of \(K_{m}\); (**b**) PPG samples (five individuals chosen at random). With the exception of PPG subject 2, which shows a clear trend towards likely aperiodic behavior, in all other respects, a slight drift remains within a dynamic regime closer to the quasi-periodic behavior. In order to analyze the dynamics of nonlinear coupling on quasi-periodic modulation, we define the multiscale \(K_{m}\equiv K_{m,t}\) parameter, conceptually inherited from [PERSON] et al. [53], to evaluate how the dynamics of the PPG signal behaves on large timescales. Figure 4a shows how the reference signals preserve a dynamic behavior virtually identical to any scale. However, the findings indicate that on a large timescale, all PPG signals show that \(K_{m,t}\approx 1\), as illustrated in Figure 4b, may give the idea that the coupling dynamics are chaotic, according to the native 0-1 test. We examine the Maximal Lyapunov Exponent (MLE) and PPG signals' fractal dimension to confirm this assumption. If a fractal dimension is a fractional number, that is a non-integer number, and the MLE is a positive or negative number. However, very close to zero, the dynamics of the PPG signal, on a large timescale, would a priori resemble the typical behavior of SNAs [52].