Study	Nonlinear Measure	Parameters Used	Signal/Domain	Key Findings
Aßmann et al. (2006, 2007) [43,44].	Symbolic Dynamics	Binary encoding of limb positions (arms <60°/≥60°; legs <120°/≥120°) 16 configurations	3D kinematic data (multi-joint, whole-body)	Limited set of preferred configurations with high recurrence, suggesting reference states
	Recurrence Plot (RP)	Embedding dimension m = 4; delay τ ≈ 10–20 frames; radius ε ≈ 30 (normalized units); sliding window ≈ 300 samples	3D joint angle time series from 4 limbs	Visual recurrence structures supported the existence of stable configuration states and intermittent transitions.
	Recurrence-based analysis: RP and RQA	m = 4 τ ≈ 10–20 frames; ε ≈ 30 Sliding window (~300 samples)	Multidimensional joint angle time series	Presence of stable states and intermittent transitions
	RQA indices	RQA indices extracted from recurrence plots, including: ✓ Recurrence rate (RR) ✓ Determinism (DET) ✓ Laminarity (LAM) ✓ Trapping time (TT) ✓ Entropy (ENTR)	Multidimensional joint angle time series	Evidence of hierarchical and self-organised motor behavior.
Ohgi et al. (2007) [56]	FNN	Delay (τ) = 250 ms (first zero of autocorrelation/first minimum of mutual information) r = 10	3D linear acceleration time series (x, y, z axes)	Spontaneous upper-limb movements displayed chaotic nonlinear dynamics with optimal embedding dimensions of 5–6, indicating deterministic structure and multiple active degrees of freedom.
	LyE	Kantz algorithm m = 5 Delay (τ) = 250 ms neighborhood radius ε = 1/10 SD		Positive LyE values across all axes confirm chaotic behavior in newborns’ spontaneous movements.
	MI	Delay (τ) selected from the first minimum of mutual information (~250 ms)		Confirmed time-dependent structure in spontaneous movement signals and supported appropriate embedding parameter selection.
	RP	m = 5 Delay (τ) = 250 ms Threshold ε small (visual inspection; no RQA metrics)		Recurrence plots revealed intermittent alternations between quiescent and bursting phases, indicating nonstationary and self-organized dynamics.
	Surrogate Data Test	Amplitude-adjusted Fourier Transform (AAFT); 100 surrogate datasets		Prediction error was significantly lower in original data than in surrogate data (p < 0.05), confirming a nonlinear deterministic origin of spontaneous movements.
Ohgi et al. (2008) [57].	FNN	Same as 2007	3D linear acceleration time series (x, y, z axes)	Infants with brain injuries exhibited significantly higher embedding dimensions than infants without brain injuries, indicating larger dimensionality and increased degrees of freedom, consistent with reduced organization of motor control.
	LyE	Same as 2007		LyE values were positive in all infants, confirming chaotic dynamics. Infants with brain injuries showed significantly higher LyE values across all axes, reflecting greater instability and unpredictability of spontaneous movements.
	MI	Same as 2007		Confirmed time-dependent structure of spontaneous movement signals and supported consistent embedding parameter selection.
	RP	Same as 2007		Recurrence plots revealed intermittent alternations between quiescent and bursting phases, indicating nonstationary and self-organized movement dynamics.
	Surrogate Data Test	Same as 2007		Prediction errors were significantly lower in original data than in surrogate data for most infants, confirming nonlinear deterministic dynamics. In a subset of infants with brain injuries, surrogate tests failed, suggesting loss of chaotic structure and increased randomness.
Dusing et al. (2009) [58].	ApEn	m = 2; Tolerance r = 0.2 × SD of the signal Delay (τ) = 1	CoP displacement time series (caudal-cephalic, medial-lateral, and resultant	Infants born preterm exhibited significantly lower ApEn values in the caudal–cephalic direction compared with infants born at full term, indicating more predictable and less complex postural control patterns.
	Surrogate Data Analysis	Surrogate generation using algorithms described by Theiler et al. ApEn calculated for original and surrogate time series Determinism was inferred when original ApEn values were significantly lower than surrogate ApEn values, indicating structured (non-random) temporal organization		Surrogate analysis demonstrated that CoP fluctuations in both preterm and full-term infants were deterministic rather than random, supporting the use of nonlinear analysis to characterize infant postural control.
Gima et al. (2011) [59].	FNN	m determined using FNN method Delay (τ) = 250 ms (first zero of the autocorrelation function	3D linear acceleration time series (x, y, z axes) of the lower extremities	The optimal embedding dimension was greater than 5 across all ages and limbs, with developmental changes showing a U-shaped pattern (6–7 at birth, decreasing to 5, then increasing again by 6 months), consistent with modulation of degrees of freedom during development.
	LyE	Kantz algorithm m = 5; Delay (τ) = 250 ms Noise reduction applied prior to estimation		Positive LyE values were observed across all ages and limbs (range: 0.79–2.99), confirming chaotic dynamics in spontaneous lower extremity movements throughout early infancy.
	MI	MI calculated between right and left lower extremity acceleration directions Low-acceleration periods excluded from analysis		Mutual information was highest at birth and decreased to its lowest values between 3 and 4 months of age, indicating developmental changes in interlimb coordination and coupling.
Smith et al. (2011) [60].	ApEn	m = 2 Tolerance (r) = 0.2 × SD of the signal Delay (τ) = 1 sample Time series length: 6147 samples (102.5 s)	Hip sagittal plane angle time series	Infants with myelomeningocele exhibited significantly lower ApEn values than infants with typical development across all ages, indicating more regular and less complex spontaneous leg movements. Lower ApEn values were associated with higher lesion levels and later onset of independent walking, supporting ApEn as a sensitive marker of impaired neuromotor control.
	Surrogate Data Analysis	Surrogate datasets generated using Chaos Data Analyzer software LyE computed for original and surrogate signals Determinism inferred when original LyE values differed significantly from surrogate values	Hip sagittal plane angle time series	Surrogate analysis confirmed that the hip angle time series were deterministic rather than random, validating the application of nonlinear analysis methods such as ApEn.
Dusing et al. (2013, 2014, 2016) [62,63,64].	ApEn	m = 2; Delay (τ) = 1 sample Tolerance (r) = 0.2 × SD of the signal Time series length: 500 samples (100 s)	CoP displacement time series (cranio–caudal, medio–lateral, and resultant)	2013: Postural control complexity was highest early in development and decreased as infants acquired midline head control and early reaching behaviors, particularly in the cranio–caudal direction. Changes in complexity occurred even when the magnitude of postural variability remained unchanged, supporting the role of temporal structure in the emergence of early motor behaviors. During early development. 2014: Infants born preterm exhibited significantly lower postural complexity, particularly in the medio–lateral direction, during the development of midline head control and reaching compared with infants born full term. Differences in complexity were evident before delays were detectable using standard clinical assessments, indicating that nonlinear measures captured subtle alterations in postural control strategies associated with prematurity. 2016: Infants born preterm demonstrated delayed adaptation of postural variability to task demands, particularly in the caudal–cephalic direction, while postural complexity remained unchanged across conditions and age. These findings indicate reduced adaptive postural control during early infancy, despite preservation of non-repetitive postural strategies.
Gima et al. (2013) [61].	FNN	Optimal embedding dimension estimated using the FNN method Delay (τ) = 250 ms (first zero of the autocorrelation function)	3D linear acceleration time series (x, y, z axes) of the right upper extremity	Infants with brain injuries exhibited significantly higher OED values at 3 months compared with healthy full-term infants, indicating increased dimensionality and altered organization of spontaneous upper extremity movements.
	Maximal Lyapunov Exponent (LyE)	Kantz algorithm m = 5; Delay (τ) = 250 ms Noise reduction applied prior to estimation	3D linear acceleration time series (x, y, z axes) of the right upper extremity	Positive LyE values were observed in both groups, confirming chaotic dynamics of spontaneous movements. However, infants with brain injuries showed uncorrelated developmental changes between OED and MLE across time, suggesting impaired self-organization and reduced coordination between motor system components.
Aßmann et al. (2019) [65].	Symbolic Dynamics	Input signal: radial distance of hands and feet relative to trunk reference Binary symbolic coding: 0 = proximal; 1 = distal. Four limbs combined to generate 16 symbolic configurations Configurations grouped into five configuration classes (I–V) based on spatial organization Symbolic sequences analyzed continuously over time	3D kinematic trajectories of hands and feet	Symbolic dynamics revealed a small subset of configurations with high occurrence and recurrence, indicating the presence of preferred spatial organizations in spontaneous neonatal movements.
	Symbolic Recurrence Analysis	Recurrence defined as repeated occurrence of identical symbolic configurations Sliding window analysis applied to capture time-dependent changes in recurrence patterns Recurrence quantified within and across configuration classes	Symbolic sequences derived from radial distance time series of hands and feet	Recurrence analysis demonstrated intermittent stabilization around specific configuration classes, alternating with exploratory phases, reflecting non-stationary and hierarchical organization of spontaneous motor behavior.
Marchi et al. (2020) [23].	Hjorth Parameters	Input signals: velocity time series of hands and feet Window length: 1 s, 50% overlap First and last windows discarded to avoid edge effects Hjorth parameters computed per window and averaged across windows, spatial components, and body side Separate computation for upper and lower limbs	3D kinematic trajectories: velocity time series of hands and feet	Upper-limb Mobility decreased and Complexity increased with post-term age, indicating progressive stabilization and enrichment of movement patterns during fidgety age. Lower-limb Hjorth parameters showed no significant age associations.
Wang et al. (2022) [66].	Sample Entropy (SampEn)	Embedding dimension (m): 3 Tolerance (r): 0.1 × SD of the signal Time series length: 100 s of CoP data Algorithm: Richman & Moorman	Resultant CoP time series and derived velocity and acceleration signals	SampEn resultant CoP was significantly correlated with adjusted age, decreasing with increasing age, indicating reduced movement complexity as infants matured within the fidgety period. SampEn of CoP velocity and acceleration were not significantly associated with age.
Shin et al. (2022) [67].	SampEn	m: not explicitly stated (consistent with standard SampEn implementations) r: proportional to the standard deviation of the signal (exact value not specified) SampEn computed separately for: ✓ Joint angle time series ✓ Joint angular velocity time series Computation performed using R (pracma package)	Time series of joint angles and joint angular velocities extracted from 2D video-based pose estimation during spontaneous movements	Sample entropy values of joint angles and joint angular velocities were significantly lower in infants with HINE < 60 compared with those with HINE ≥ 60 and showed positive correlations with HINE scores across most upper- and lower-limb joints. These findings indicate reduced movement complexity in infants with poorer early neurological outcomes.
Deng et al. (2023) [45].	SampEn	m = 2 r = 0.2 × SD, continuous data length ≈ 104 samples (per leg per day, 20 Hz, 8 h active data)	Lower-limb kinematic signals (ankle acceleration and angular velocity) recorded via IMUs during spontaneous movements	Infants in the AR group exhibited significantly lower SampEn values than the TD group, indicating reduced movement complexity and variability.
	Symbolic Dynamics (Barcoding States)	Number of symbolic states: 16 State probabilities calculated for each infant SampEn applied to symbolic state sequences	Discrete symbolic representations of lower-limb acceleration and angular velocity time series	The AR group showed reduced diversity of symbolic states and lower entropy of state sequences, reflecting less adaptive and less complex spontaneous movement patterns than typically developing infants.
Oh et al. (2024) [68].	Fuzzy Entropy (FuzzyEn) Sample entropy–related rationale (comparative) Linear descriptive measures (supportive)	Embedding dimension (m) = 2; tolerance (r) = 0.2; applied to concatenated peak acceleration time series FuzzyEn chosen over SampEn to allow graded similarity (fuzzy membership function)	Peak acceleration per leg movement (m/s2), derived from wearable sensor data Lower-limb kinematic time series Average leg movement rate (mov/h); peak acceleration (m/s2)	Higher fuzzy entropy values were significantly associated with higher BSID-III motor composite scores at 12 months (median quantile regression), indicating greater movement complexity in infants with better motor outcomes Entropy of movement intensity (not movement quantity) emerged as the most sensitive predictor of motor development Neither movement rate nor peak acceleration alone predicted motor, language, or cognitive outcomes
Park et al. (2024) [69].	Sample Entropy (SampEn)	m = 2 r = 0.2 × SD; time series length ≈ 3000–7000 samples (24 Hz, 3–5 min) SampEn computed separately for: ✓ Joint angle time series ✓ Joint angular velocity time series	Time series of joint angles and joint angular velocities derived from 2D video-based pose estimation during spontaneous infant movements	Infants with motor developmental delay exhibited significantly lower SampEn values across most upper- and lower-limb joints compared with infants without delay. SampEn measures showed positive correlations with motor composite scores of the BSID-III at 9 months corrected age, indicating reduced movement complexity in infants with poorer motor outcomes.