Critical Slowing Down

Early warning signals approaching a tipping point

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Critical slowing down is a universal precursor to a saddle-node bifurcation (tipping point). Near the bifurcation parameter μ → 0, the eigenvalue λ ≈ μ → 0, so perturbations decay like e^(λt) with λ → 0.
τ_recovery ∝ 1/|λ| → ∞ as μ → 0
Statistical signatures in noisy time series: Variance increases (as σ²/(2|λ|)), and autocorrelation at lag-1 → 1. These signals can warn of ecological collapses, climate tipping points, and disease onset.