Near a fold bifurcation, the restoring force weakens ("critical slowing down"): variance σ² and lag-1 autocorrelation ρ₁ both rise before the tipping point. These are universal early warning signals (EWS) for regime shifts.
The normal form of a fold bifurcation: dx/dt = μ(t) − x² + σ·ξ. As μ → 0⁻, the stable fixed point x* = √(−μ) approaches the unstable one, and the eigenvalue λ = −2√(−μ) → 0. Critical slowing down means perturbations decay slower, so variance ∝ σ²/(2|λ|) and autocorrelation ρ₁ = exp(λ·dt) both diverge. After the tipping point, the system collapses to a different state (catastrophe).