# A Review of Methods and Applications for a Heart Rate Variability Analysis
## 3 Pressure Support Ventilation (PSV)
### Non-Linear Methods  
The heart has been represented as an intricate control system [32]. Hence, the HRV description, which relies solely on linear methods, is insufficient to analyze the signals in many cases. Hence, non-linear approaches are also suggested to represent the HRVs' properties [32]. Popular non-linear methods include the Poincare plot, detrended fluctuation analysis (DFA), and recurrence plot. The Poincare plot visually represents the correlation between the consecutive RRIs (Figure 5). In the Poincare plot, an ellipse is drawn along the line of identity, and then it is tailored to the statistics points. The width (SD1) and the length (SD2) of the ellipse are used to calculate two non-linear HRV features. Such values are used as indicators of both short- and long-term variance [33]. Various non-linear techniques exist for quantifying the correlations in nonstationary physiological time series data [34]. The DFA method, developed in the 1970s, is a technique divulging correlation information. In the context of the HRV study, associations are split up into short-term and long-term variations, depending on the time frame under consideration. These variations are measured and quantified with the DFA method using parameters like alpha1 (\(\alpha\)1) and alpha2 (\(\alpha\)2), respectively [30]. The slope of the log-log graph is utilized to determine the parameters \(\alpha\)1 and \(\alpha\)2. These values offer a measurement of association (in terms of fluctuation, \(F_{\rm n}\)) that is dependent on the amount of collected data (n) (Figure 6). Figure 4: A typical AR spectrum of a 5 min HRV, plotted using LabVIEW. Figure 5: A representative Poincare graph of a 5 min HRV, plotted using LabVIEW. [PERSON] introduced the concept of recurrence at the end of the 19 th century. Recurrence is a fundamental characteristic of every deterministic dynamic scheme [35]. It refers to the phenomenon in which the stages of a dynamic scheme repeatedly appear in phase space [36]. A phase space plot is an imaginary multi-dimensional region where in every point indicates a state of the system. [PERSON]'s theorem [37] has served as the foundation for reconstructing the phase region graphs of the dynamical systems. The theorem proposes that if a variety of parameters governs the dynamics of a system, but a solitary parameter is recognized, at that point, the solitary parameter can still represent the entire dynamics of the system. However, the prediction of the entire system dynamics requires drawing a graph using the quantities of the recognized parameter compared to themselves for a definite amount of times at a predetermined time delay. The selection of appropriate quantities for the embedding dimension and the time delay plays a significant role during the rebuilding of the phase space graph of a dynamic arrangement. The visualization of the vital recurrence property of a phase space plot in two dimensions (2D) has been reported by [PERSON] et al. (1987), from whom the idea of recurrence plots was proposed [38]. A recurrence graph is typically described as a symmetrical square matrix in two dimensions. This matrix illustrates the time at which two states of the arrangement become state-space neighbors depending on a cut-off threshold space. However, the information that can be gleaned from this graph is quality-based [39; 40]. A recurrence quantification study (abbreviated as RQA) is developed to extract quantity-based variables out of the recurrence plot. The concentration of the reappearance loci and the diagonal, vertical, and horizontal lines present in the recurrence plot are employed for the extraction of quantitative parameters using the RQA method.