State-Space Attractor Morphology as a Marker of Complexity Matching in Group Heart Rate Variability Dynamics

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Complexity matching helps explain how interacting physiological systems may become coordinated during shared experiences. In this study, we investigated group-level complexity matching by reconstructing heart rate variability (HRV) dynamics from 20 participants across six intervals of a guided heart-focused session. For each participant and interval, HRV was embedded in a two-dimensional delay-coordinate space using an interval-specific optimal delay. The reconstructed attractors were then analyzed using a Convolutional neural network (CNN) autoencoder, followed by clustering of the latent representations. The analysis identified three recurrent attractor morphology types: circular or loop-like attractors (Type 1), distorted circular attractors (Type 2), and distorted concentrated attractors (Type 3). In the complete sample of 20 participants (the primary analysis), Type 2 was more prevalent during the first three intervals, whereas Type 1 became more prevalent during the later intervals and was dominant in the final interval, increasing from 10.00% in Interval 1 to 60.00% in Interval 6 (Cochran’s Q(5) = 19.46, Holm-adjusted p = 0.0047). An exploratory secondary analysis restricted to the 15 participants whose morphology classification shifted across the protocol showed a similar pattern (increase from 6.67% to 66.67%; Q(5) = 20.00, Holm-adjusted p = 0.00375). This pattern suggests increasing similarity in HRV state-space organization, consistent with group-level complexity matching. The increase in Type 1 occurred during the later, more prosocially oriented intervals of this fixed-order protocol; because interval order was confounded with elapsed time and instruction repetition, this association should not be interpreted as a causal effect of the appreciation- or compassion-focused content. Coupled Thomas–Rössler systems further illustrated how nonlinear interaction can produce increasing similarity in attractor geometry. Compared with our earlier H-rank-based approach, the present method analyzes participant-specific reconstructed HRV attractor morphology using unsupervised CNN-autoencoder-based feature extraction and clustering. These findings suggest that attractor reconstruction and CNN-autoencoder-based clustering can reveal collective physiological organization that is not visually apparent in the raw HRV recordings. Whether conventional time-domain, frequency-domain, or entropy-based HRV indices would detect a comparable pattern was not directly tested here and remains an open question for future work.

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