From Stability to Complexity: A Systematic Review of Long-term Divergence Exponents in Nonlinear Gait Analysis

BackgroundDivergence exponents (DE), or maximum Lyapunov exponents, computed from stride-to-stride fluctuations have traditionally been interpreted as measures of gait stability. However, evidence suggests this measure may also reflect gait complexity and automaticity. This systematic review evaluated empirical support for reinterpreting long-term DE as a complexity measure. MethodsWe systematically searched Web of Science databases through January 2026 for studies applying Rosensteins algorithm to human gait. We systematically extracted experimental conditions, and participant characteristics from each study. Study quality was assessed using a framework evaluating analytical rigor, outcome reporting, and sample size adequacy. We conducted a meta-analysis examining correlations between long-term DEs and detrended fluctuation analysis (DFA) scaling exponents, and synthesized evidence from perturbation (environmental disturbances), cueing (external rhythmic stimuli), and between-subject (clinical vs control) studies. ResultsSixty-two studies published between 2000 and 2026 met inclusion criteria, with 44% achieving high overall quality scores. Meta-analysis from six datasets (209 participants) revealed a positive correlation between long-term DE and DFA scaling exponents (r=0.64, 95% CI 0.34 to 0.82; I{superscript 2}=82%). Perturbation studies consistently showed increased short-term DE (lower local stability) while simultaneously decreasing long-term DE by up to 51%. External auditory and visual cueing interventions induced long-term DE decreases (up to -86%) while minimally affecting short-term DEs. Between-subject comparisons revealed heterogeneous patterns, with clinical populations exhibiting both increases and decreases in long-term DE depending on pathology. ConclusionsConverging meta-analytic and experimental evidence supports reinterpreting long-term DE as the Attractor Complexity Index--a measure of gait complexity and automaticity rather than stability. Reduced long-term DE during controlled gait conditions reflects suppression of low-frequency variations in gait variability, which constrains phase space exploration and accelerates divergence curve saturation. The measures sensitivity to prefrontal cortex engagement and attentional demands reveals that long-term DE captures the degree of gait automaticity, with lower values indicating a shift from automatic subcortical control to executive function-mediated regulation. This attention-dependent control reorganization explains patterns observed in aging, clinical populations, and experimental perturbations. This paradigm shift establishes long-term DE as a complementary biomarker for motor-cognitive aspects of gait control, with implications for fall risk assessment, disease monitoring, and rehabilitation evaluation.