## 2 Materials and Methods
### Rqa
#### 2.4.2 Recurrence Plot  
A trajectory visualization in phase space with more than three dimensions is challenging. Therefore, [PERSON] [38] presented the so-called recurrence plots. These plots are a fundamental RQA tool that enables the visualization of multidimensional phase space in a two-dimensional plot. In the plot, the recurrence states recorded by \"ones\" are recorded in the matric format. Those states that are not recurrent are recorded with \"zeros\". The recurrence state is possible to determine by the set threshold distance \(\epsilon\), see Formula (7). According to the [34], it is possible to express the recurrence plot as:  
\[R_{i,j}=\Theta(\epsilon-||x_{i}-x_{j}||),\text{ for }i,j=1,2,...,N, \tag{6}\]  
where \(\Theta\) is Heaviside function, can be a value 1 and 0 according to Formula (7):  
\[R_{i,j}=0\text{ for }||x_{i}-x_{j}||>\epsilon;\text{ and }R_{i,j}=1\text{ for }||x_{i}-x_{j}||\leq\epsilon, \tag{7}\]  
where \(R_{i,j}\) marks a point in a matrix \(R\) in time \(i\) and other time \(j\), \(x_{i}\) and \(x_{j}\) are individual states of the system, \(N\) is the total number of states, \(||.||\) is a distance of two states in a phase space and \(\epsilon\) is a threshold distance [34].  
A graphic representation of matrix \(R\) is the recurrence plot. Points with value 1 in the matrix represent the recurrence states. It is possible to encounter also a non-binary (colored) version of the recurrence plot, in which the distances in between the individual states (points) in the phase space are placed and, at the same time, the Heaviside function was not used. This procedure avoids entering a threshold distance, i.e., a graphic representation of the distance matrix. In the graph legend, there is a so-called colormap that defines what color corresponds to what distance.  
A disadvantage of the recurrence plots is their mathematical complexity due to the paired \(t\)-test of all states. \(N^{2}\) tests are counted for \(N\) states. In its very nature, the recurrence plot is always symmetrical, according to the main diagonal line. In addition, basic structures appear. These structures include separate points, diagonal lines, and vertical and horizontal lines, respectively. Each of these structures has its meaning [34].  
Distant points represent unique points in the phase space, in which the system does not remain long. Diagonal lines mark the trajectories going through the same area in the phase space at a different time. Diagonal lines are characteristic of its determinism. Vertical and horizontal lines mark system remaining in one point or that might change very slowly [35]. Recurrence plot topology is depicted in Figure 3.  
The most important part when creating the recurrence plot is choosing the right threshold value. Recent studies discuss the optimal threshold value [39, 40, 41] because only the slightest change in threshold distance might dramatically affect the outcomes [40]. A frequently used method of setting the threshold distance is setting the threshold distance value perceptually from the maximal distance in the phase space. Another used method focuses on such value that would not exceed 10% of the average or maximal distance in the phase space [39]. A fixed percentage of recurrence points is another method of setting the threshold value. To ensure this exact percentage of recurrence points, a certain threshold distance value is set [39]. Often, this value is 1% [39, 40]. It is possible to see also different setting, e.g., 5% [42].  
Other recommended settings include the threshold value \(\epsilon=0.1\sigma\) (\(\sigma\) is the standard deviation of signal input). This setting was set by Prof [PERSON] as a result of an experiment [41].