$Recovery — x(t) = x_eq + (x₀-x_eq)e^{-t/τ} + overshoot$ Tap to zoom

Recovery

x(t) = x_eq + (x₀-x_eq)e^{-t/τ} + overshoot

Damped recovery with overshoot — the system swings past equilibrium before settling. The overshoot is the extra.

Swinging past center before settling into something new

Part of: RESILIENCE

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Forged — σ_y(ε) = σ₀ + Kε^n

Forged

σ_y(ε) = σ₀ + Kε^n

Growth — dN/dt = r(K' - N), K' > K

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dN/dt = r(K' - N), K' > K

$Phoenix — f(t) = A(1 - e^{-t/τ₁})e^{t/τ₂}, τ₂ > τ₁$

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f(t) = A(1 - e^{-t/τ₁})e^{t/τ₂}, τ₂ > τ₁

$Repair — G(t) = G₀(1 - e^{-t/τ_r}) · H(t-t_d)$

Repair

G(t) = G₀(1 - e^{-t/τ_r}) · H(t-t_d)