## 3 Method and Materials
### 0-1 Test Algorithm  
Summarising the main items of the modified version of the 0-1 test method [31], Table 1 shows the four steps to be followed. The actions of the algorithm would be:  
1. Equation (1) is solved for a given \(c\in(0,2\pi)\). 2. Equation (2) is computed with \(p_{c}(n)\) and \(q_{c}(n)\) of the previous step to analyze the diffusive or non-diffusive behavior. [PERSON] and [PERSON] [32] propose an expression similar to Equation (2), regarding asymptotic behavior, with best convergence properties. 3. The asymptotic growth rate \(K_{c}\) of \(M_{c}(n)\), makes it possible to distinguish between regular behavior and chaotic behavior. There are two suggested methods for deter mining \(K_{c}\): regression method and correlation method. However, the correlation method provides better results than the regression method, according to the analyses carried out, for different dynamic systems, by [PERSON] and [PERSON] [32]. In our study, we have used both types of methods, and we have verified that the correlation method yields better results. 4. Steps 1 to 3 are repeated for several values of \(c\); with 100 \(c\) values, selected randomly, it is enough [32], to ensure a higher degree of convergence of the statistic. The final result, \(K\), attends to the median of the computed \(K_{c}\) values, that is, \(K=\text{median}(K_{c})\). In this study, we introduce a slight modification to the original method, our modified version of the test, taking the median of the absolute value of the calculated \(K_{c}\) values, after removing outliers values, i.e., \(K_{m}=\text{median}(|K_{c}|)\), since the interest is focused not so much on the numerical values as on the strength of the correlation. It also enables us to identify intermediate dynamics, as we shall see below. With either method, regression or correlation method, and our modified version of the 0-1 test, a \(K_{m}\approx 0\) value indicates a regular dynamic, and a value of \(K_{m}\approx 1\) suggests an aperiodic behavior. However, the test cannot distinguish between random behavior and chaotic behavior, as we will see later. Commonly, enough length of a time series is claimed in any chaos identification mechanism so that the attractor can fully develop itself, and, hence, the asymptotic behavior of the underlying system, whether diffusive or not, can be clearly identified. If the length of the time series under study is short, it is within the possibility that the asymptotic behavior, diffusive or not, lacks the expected dominant effect. In this case, more than \(K_{m}\)'s convergence towards 0 or 1, \(K_{m}\)'s trend towards 0 or 1, concerning the length of the time series, is examined to dictate the presence or absence of more complex dynamics. Although the complexity of signals admits different definitions, without overlooking the influence of the data acquisition system--a rigorous definition has not been agreed by the scientific community [33; 34]--a consistent alternative evaluates the degree of complexity regarding regularity in the patterns of repetition of the data; to some extent, this alternative quantifies the difficulty in describing or understanding a signal [18]. These patterns lead to an ordering of the signals between two opposite ends, the most regular or periodic, and the most irregular or random, with a whole range of intermediate dynamic options; as a dynamic variant approaches a most irregular regime, as in the case of a chaotic signal, it acquires greater degrees of freedom or versatility, without losing determinism in its dynamic behavior.