A noise-robust Koopman spectral analysis of an intermittent dynamics method for complex systems: a case study in pathophysiological processes of obstructive sleep apnea

Abstract

Koopman operator theory and the Hankel alternative view of the Koopman (HAVOK) model have been widely used to investigate the chaotic dynamics in complex systems. Although the statistics of intermittent dynamics have been evaluated in the HAVOK model, they are not adequate to characterize intermittent forcing. In this paper, we propose a novel method to characterize the intermittent phases, chaotic bursts, and local spectral-temporal properties of various intermittent dynamics modes using spectral decomposition and wavelet analysis. To validate our methods, we compared the sensitivity to noise level and sampling period of the HAVOK and our proposed method in the Lorenz system. Our results show that the prediction accuracy of lobe switching and the intermittent forcing identifiability were highly sensitive to the sampling rate. While it is possible to maintain the desired accuracy in high noise-level cases with an appropriately selected rank in the HAVOK model, our proposed method is demonstrated to be more robust. To show the applicability of our proposed method, obstructive sleep apnea—a complex pathological disorder—was selected as a case study. The results show a strong association between active forcing and the hypopnea-apnea events. Our proposed method has been demonstrated to be a promising data-driven method to provide key insights into the dynamics of complex systems.