## 5 Conclusions  
Applying the 0-1 test to the reference signals--periodic, quasi-periodic, aperiodic, chaotic, and random signals--and evaluating a modified version of the test, we show how to describe the dynamics of a biological signal: in our case, the PhotoPlethysmoGraphic (PPG) signal. The analysis has been carried out at different timescales to extract the distinct and relevant dynamics present. Only five subjects are shown in the main body of this paper, while the Accompanying Material (see Appendix A) covers the main results of the 40 subjects that make up the dataset. With the modified 0-1 test, we described the PPG signal behavior of 40 young, healthy subjects as mainly quasi-periodic on a small timescale. On large timescales, and after conducting a preliminary analysis, we feel that the PPG signals describe a nonchaotic but strange behavior. On a small timescale, the quasi-periodic dynamics imposed by the cardiorespiratory system prevail. Still, on a large timescale, other factors related to the cardiovascular system come into play. These factors force nonlinearly the quasi-periodic dynamics and generate more complex and versatile dynamics that contribute to a heart rate more easily adaptive to changing conditions of the organism in its psychosomatic relationship with the surrounding environment. So far, on empirical data, the modified 0-1 test does not distinguish between a chaotic signal and a random (stochastic) signal nor does it differentiate between a chaotic signal and the characteristic dynamics of a strange nonchaotic attractor, since both dynamics are aperiodic, due to the fractal nature of its geometric structure. Therefore, the difference between a chaotic attractor and a strange nonchaotic attractor does not meet its geometric structure but rather its dynamic evolution. A (strange) chaotic attractor is characterized by the sensitivity to initial conditions, say, two initially close together trajectories diverge exponentially with time. In the case of a strange nonchaotic attractor, two initially close together trajectories do not diverge exponentially with time, even though each trajectory may have an arbitrarily complex form, so their prediction horizon (predictability) is much wider. We think that the behavior of the PPG signal, on a large timescale and in the case of healthy young people, is due to the characteristic evolution of a strange nonchaotic attractor, \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Evaluated Signal**} & **Maximal Lyapunov Exponent (MLE)** & **Fractal Dimension** \\ \cline{2-3}  & \(\lambda_{max}\) & \(D_{F}\) \\ \hline subject number 1 (PPG1) & \(-0.0254\) & \(1.1168\) \\ \hline subject number 2 (PPG2) & \(-0.0488\) & \(1.1937\) \\ \hline subject number 3 (PPG3) & \(-0.0290\) & \(1.2112\) \\ \hline subject number 4 (PPG4) & \(+0.0002\) & \(1.1730\) \\ \hline subject number 5 (PPG5) & \(-0.0419\) & \(1.1655\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximal Lyapunov exponent (\(\lambda_{max}\)) and fractal dimension (\(D_{F}\)), of the PPG signals, acquired from five individuals chosen at random. as is shown by the maximal Lyapunov exponents and the Hurst exponents presented in this work. It is likely that under specific triggers, such as stress situations, the coupling between the different subsystems that make up the cardiorespiratory system will undergo a transition to chaos from a quasi-periodic dynamic. This transition should take place through a strange nonchaotic attractor, as evidenced in different physical [55] and biological systems [56]. Future work will delve into this intriguing bifurcation between regular behavior and presumed chaotic behavior and what physiological consequences could follow from it in the sphere of the PPG signal analysis or indicators related to it. The PPG signal dynamic behavior analysis moves away from the conventional morphological analysis of the PPG signal, whereby changes in different morphological indicators correlate with cardiovascular disorders and ageing.