Table 4: Advantages and limitations of phase space diagram, power spectrum, Poincaré map, and Lyapunov exponent methods.


Phase space (i) It allows intuitively visualizing the respiration stability.(i) Quantitative analysis is difficult (threshold value cannot be set).
(ii) Visual grading is difficult for equivocal patterns.
(iii) Analysis becomes difficult when regularities of amplitude, frequency, and baseline position are discordant or when the respiratory pattern consists of regular and irregular patterns.

Power spectrum(i) Stability is rated based on frequency.
(ii) Both visual and quantitative analyses are possible.
(i) Information on amplitude and baseline position cannot be obtained.

Poincaré map(i) It uses the shape and directionality of distribution patterns in Poincaré map as differential points and allows easy analysis of the cases in which the amplitude and baseline position are discordant.
(ii) Both visual and quantitative analysis are possible.
(i) It cannot get information about frequency.
(ii) Various Poincaré maps can be generated depending on various fitting and sectioning methods.

Lyapunov exponent(i) Respiration is evaluated in terms of the temporal divergence or convergence.(i) It is not correlated with phase space, power spectrum, and Poincaré map methods.