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Journal of Applied Nonlinear Dynamics 14(4) (2025) 973--980 | DOI:10.5890/JAND.2025.12.015

Kazimieras Pukenas

Department of Health Promotion and Rehabilitation, Lithuanian Sports University, Sporto 6, LT-44221, Kaunas, Lithuania

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Abstract

A new algorithm is described for detecting small changes in the topological structure of the dynamics of a nonlinear system due to perturbations in the driving signals. The proposed approach is based on implementing a covariance-based clustering method on the windowed training dataset of the reconstructed phase space of the dynamical system, and change-point is detected by evaluating the minimum Euclidean distance between all centroids of these clusters and the windowed covariance matrices for the testing data. Applying the proposed approach to the Rössler system, the Hénon-Heiles system and a photoplethysmogram signal when applying small transient perturbations showed its effectiveness at detecting small discontinuities in the dynamics of the system even when the system is chaotic.

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