We integrated visual and quantitative methods for analyzing the stability of respiration using four methods: phase space diagrams, Fourier spectra, Poincaré maps, and Lyapunov exponents. Respiratory patterns of 139 patients were grouped based on the combination of the regularity of amplitude, period, and baseline positions. Visual grading was done by inspecting the shape of diagram and classified into two states: regular and irregular. Quantitation was done by measuring standard deviation of x and v coordinates of Poincaré map (SD x , SD v ) or the height of the fundamental peak (A1) in Fourier spectrum or calculating the difference between maximal upward and downward drift. Each group showed characteristic pattern on visual analysis. There was difference of quantitative parameters (SD x , SD v , A1, and MUD-MDD) among four groups (one way ANOVA, p = 0.0001 for MUD-MDD, SD x , and SD v , p = 0.0002 for A1). In ROC analysis, the cutoff values were 0.11 for SD x (AUC: 0.982, p < 0.0001), 0.062 for SD v (AUC: 0.847, p < 0.0001), 0.117 for A1 (AUC: 0.876, p < 0.0001), and 0.349 for MUD-MDD (AUC: 0.948, p < 0.0001). This is the first study to analyze multiple aspects of respiration using various mathematical constructs and provides quantitative indices of respiratory stability and determining quantitative cutoff value for differentiating regular and irregular respiration.